 6.6.1: Verify the identity.
 6.6.2: Verify the identity.
 6.6.3: Verify the identity.
 6.6.4: Verify the identity.
 6.6.5: Verify the identity.
 6.6.6: Verify the identity.
 6.6.7: Verify the identity.
 6.6.8: Verify the identity.
 6.6.9: Verify the identity.
 6.6.10: Verify the identity.
 6.6.11: Verify the identity.
 6.6.12: Verify the identity.
 6.6.13: Verify the identity.
 6.6.14: Verify the identity.
 6.6.15: Verify the identity.
 6.6.16: Verify the identity.
 6.6.17: Verify the identity.
 6.6.18: Verify the identity.
 6.6.19: Verify the identity.
 6.6.20: Verify the identity.
 6.6.21: Verify the identity.
 6.6.22: Verify the identity.
 6.6.23: Verify the identity.
 6.6.24: Verify the identity.
 6.6.25: Verify the identity.
 6.6.26: Verify the identity.
 6.6.27: Verify the identity.
 6.6.28: Verify the identity.
 6.6.29: Verify the identity.
 6.6.30: Verify the identity.
 6.6.31: Verify the identity.
 6.6.32: Verify the identity.
 6.6.33: Verify the identity.
 6.6.34: Verify the identity.
 6.6.35: Verify the identity.
 6.6.36: Verify the identity.
 6.6.37: Verify the identity.
 6.6.38: Verify the identity.
 6.6.39: Verify the identity.
 6.6.40: Verify the identity.
 6.6.41: Verify the identity.
 6.6.42: Verify the identity.
 6.6.43: Verify the identity.
 6.6.44: Verify the identity.
 6.6.45: Verify the identity.
 6.6.46: Verify the identity.
 6.6.47: Verify the identity.
 6.6.48: Verify the identity.
 6.6.49: Verify the identity.
 6.6.50: Verify the identity.
 6.6.51: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.52: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.53: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.54: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.55: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.56: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.57: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.58: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.59: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.60: Show that the equation is not an identity. (Hint: Find one number f...
 6.6.61: Either show that the equation is an identity or show that the equat...
 6.6.62: Either show that the equation is an identity or show that the equat...
 6.6.63: Either show that the equation is an identity or show that the equat...
 6.6.64: Either show that the equation is an identity or show that the equat...
 6.6.65: Refer to Example 6. Make the trigonometric substitution x a sin for...
 6.6.66: Refer to Example 6. Make the trigonometric substitution x a sin for...
 6.6.67: Refer to Example 6. Make the trigonometric substitution x a sin for...
 6.6.68: Refer to Example 6. Make the trigonometric substitution x a sin for...
 6.6.69: Make the trigonometric substitution x a tan for /2 < < /2 and a > 0...
 6.6.70: Make the trigonometric substitution x a tan for /2 < < /2 and a > 0...
 6.6.71: Make the trigonometric substitution x a tan for /2 < < /2 and a > 0...
 6.6.72: Make the trigonometric substitution x a tan for /2 < < /2 and a > 0...
 6.6.73: Make the trigonometric substitution x a sec for 0 < < /2 and a > 0....
 6.6.74: Make the trigonometric substitution x a sec for 0 < < /2 and a > 0....
 6.6.75: Make the trigonometric substitution x a sec for 0 < < /2 and a > 0....
 6.6.76: Make the trigonometric substitution x a sec for 0 < < /2 and a > 0....
 6.6.77: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.78: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.79: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.80: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.2.1: Find all solutions of the equation.
 6.6.2.2: Find all solutions of the equation.
 6.6.2.3: Find all solutions of the equation.
 6.6.2.4: Find all solutions of the equation.
 6.6.2.5: Find all solutions of the equation.
 6.6.2.6: Find all solutions of the equation.
 6.6.2.7: Find all solutions of the equation.
 6.6.2.8: Find all solutions of the equation.
 6.6.2.9: Find all solutions of the equation.
 6.6.2.10: Find all solutions of the equation.
 6.6.2.11: Find all solutions of the equation.
 6.6.2.12: Find all solutions of the equation.
 6.6.2.13: Find all solutions of the equation.
 6.6.2.14: Find all solutions of the equation.
 6.6.2.15: Find all solutions of the equation.
 6.6.2.16: Find all solutions of the equation.
 6.6.2.17: Find all solutions of the equation.
 6.6.2.18: Find all solutions of the equation.
 6.6.2.19: Find all solutions of the equation.
 6.6.2.20: Find all solutions of the equation.
 6.6.2.21: Find all solutions of the equation.
 6.6.2.22: Find all solutions of the equation.
 6.6.2.23: Find all solutions of the equation.
 6.6.2.24: Find all solutions of the equation.
 6.6.2.25: Find all solutions of the equation.
 6.6.2.26: Find all solutions of the equation.
 6.6.2.27: Find all solutions of the equation.
 6.6.2.28: Find all solutions of the equation.
 6.6.2.29: Find all solutions of the equation.
 6.6.2.30: Find all solutions of the equation.
 6.6.2.31: Find all solutions of the equation.
 6.6.2.32: Find all solutions of the equation.
 6.6.2.33: Find all solutions of the equation.
 6.6.2.34: Find all solutions of the equation.
 6.6.2.35: Find all solutions of the equation.
 6.6.2.36: Find all solutions of the equation.
 6.6.2.37: Find all solutions of the equation.
 6.6.2.38: Find all solutions of the equation.
 6.6.2.39: Find all solutions of the equation.
 6.6.2.40: Find all solutions of the equation.
 6.6.2.41: Find all solutions of the equation.
 6.6.2.42: Find all solutions of the equation.
 6.6.2.43: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.44: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.45: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.46: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.47: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.48: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.49: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.50: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.51: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.52: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.53: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.54: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.55: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.56: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.57: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.58: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.59: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.60: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.61: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.62: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.63: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.2.64: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.65: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.66: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.67: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.68: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.69: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.70: Find the solutions of the equation that are in the interval [0, 2 )...
 6.6.2.71: Approximate, to the nearest 10, the solutions of the equation in th...
 6.6.2.72: Approximate, to the nearest 10, the solutions of the equation in th...
 6.6.2.73: Approximate, to the nearest 10, the solutions of the equation in th...
 6.6.2.74: Approximate, to the nearest 10, the solutions of the equation in th...
 6.6.2.75: Approximate, to the nearest 10, the solutions of the equation in th...
 6.6.2.76: Approximate, to the nearest 10, the solutions of the equation in th...
 6.6.2.77: Tidal waves A tidal wave of height 50 feet and period 30 minutes is...
 6.6.2.78: Temperature in Fairbanks The expected low temperature T (in F) in F...
 6.6.2.79: Temperature in Chicago The average monthly high temperature T (in F...
 6.6.2.80: Temperature in Augusta The average monthly high temperature T (in F...
 6.6.2.81: Intensity of sunlight On a clear day with D hours of daylight, the ...
 6.6.2.82: Intensity of sunlight Refer to Exercise 81. On cloudy days, a bette...
 6.6.2.83: Protection from sunlight Refer to Exercises 81 and 82. A dermatolog...
 6.6.2.84: Highway engineering In the study of frost penetration problems in h...
 6.6.2.85: Rabbit population Many animal populations, such as that of rabbits,...
 6.6.2.86: River flow rate The flow rate (or water discharge rate) at the mout...
 6.6.2.87: Shown in the figure is a graph of for . Using calculus, it can be s...
 6.6.2.88: Shown in the figure is the graph of the equationThe xcoordinates o...
 6.6.2.89: If I(t) is the current (in amperes) in an alternating current circu...
 6.6.2.90: If I(t) is the current (in amperes) in an alternating current circu...
 6.6.2.91: Approximate the solution to each inequality on the interval [0, 2 ].
 6.6.2.92: Approximate the solution to each inequality on the interval [0, 2 ].
 6.6.2.93: Approximate the solution to each inequality on the interval [0, 2 ].
 6.6.2.94: Approximate the solution to each inequality on the interval [0, 2 ].
 6.6.2.95: Graph f in the viewing rectangle [0, 3] by [1.5, 1.5]. (a) Approxim...
 6.6.2.96: Graph f in the viewing rectangle [0, 3] by [1.5, 1.5]. (a) Approxim...
 6.6.2.97: Because planets do not move in precisely circular orbits, the compu...
 6.6.2.98: Because planets do not move in precisely circular orbits, the compu...
 6.6.2.99: Because planets do not move in precisely circular orbits, the compu...
 6.6.2.100: Because planets do not move in precisely circular orbits, the compu...
 6.6.2.101: Estimate the solutions of the equation in the interval [ , ]. sin 2...
 6.6.2.102: Estimate the solutions of the equation in the interval [ , ]. cos3 ...
 6.6.2.103: Estimate the solutions of the equation in the interval [ , ]. ln 1 ...
 6.6.2.104: Estimate the solutions of the equation in the interval [ , ]. esin ...
 6.6.2.105: Estimate the solutions of the equation in the interval [ , ]. 3 cos...
 6.6.2.106: Estimate the solutions of the equation in the interval [ , ]. cos 2...
 6.6.2.107: Weight at various latitudes The weight W of a person on the surface...
 6.6.3.1: Express as a cofunction of a complementary angle.
 6.6.3.2: Express as a cofunction of a complementary angle.
 6.6.3.3: Express as a cofunction of a complementary angle.
 6.6.3.4: Express as a cofunction of a complementary angle.
 6.6.3.5: Find the exact values.
 6.6.3.6: Find the exact values.
 6.6.3.7: Find the exact values.
 6.6.3.8: Find the exact values.
 6.6.3.9: Find the exact values.
 6.6.3.10: Find the exact values.
 6.6.3.11: Express as a trigonometric function of one angle.cos 70 cos 53sin 7...
 6.6.3.12: Express as a trigonometric function of one angle. cos 6 cos 25sin 6...
 6.6.3.13: Express as a trigonometric function of one angle.cos 61 sin 82sin 6...
 6.6.3.14: Express as a trigonometric function of one angle.sin 57 cos 4cos 57...
 6.6.3.15: Express as a trigonometric function of one angle.cos 3 sin 2 cos 2 ...
 6.6.3.16: Express as a trigonometric function of one angle.sin 5 cos 2 cos 5 ...
 6.6.3.17: Use the given conditions to find the exact value of the expression.
 6.6.3.18: Use the given conditions to find the exact value of the expression.
 6.6.3.19: Use the given conditions to find the exact value of the expression.
 6.6.3.20: Use the given conditions to find the exact value of the expression.
 6.6.3.21: Use the given conditions to find the exact value of the expression.
 6.6.3.22: Use the given conditions to find the exact value of the expression.
 6.6.3.23: If and are acute angles such that and , find(a) (b)(c) the quadrant...
 6.6.3.24: If and are acute angles such that and , find(a) (b)(c) the quadrant...
 6.6.3.25: If and for a thirdquadrant angle and a firstquadrant angle , find...
 6.6.3.26: If and for a secondquadrant angle and a thirdquadrant angle , fin...
 6.6.3.27: If and are thirdquadrant angles such that and , find(a) (b)(c) the...
 6.6.3.28: If and are secondquadrant angles such that and , find(a) (b)(c) th...
 6.6.3.29: Verify the reduction formula.
 6.6.3.30: Verify the reduction formula.
 6.6.3.31: Verify the reduction formula.
 6.6.3.32: Verify the reduction formula.
 6.6.3.33: Verify the reduction formula.
 6.6.3.34: Verify the reduction formula.
 6.6.3.35: Verify the reduction formula.
 6.6.3.36: Verify the reduction formula.
 6.6.3.37: Verify the reduction formula.
 6.6.3.38: Verify the reduction formula.
 6.6.3.39: Verify the reduction formula.
 6.6.3.40: Verify the reduction formula.
 6.6.3.41: Verify the identity.
 6.6.3.42: Verify the identity.
 6.6.3.43: Verify the identity.
 6.6.3.44: Verify the identity.
 6.6.3.45: Verify the identity. cos u v cos u v 2 cosu cos v
 6.6.3.46: Verify the identity.sin u v sin u v 2 sin u cos v
 6.6.3.47: Verify the identity. sin u v sin u v sin2 u sin2 v
 6.6.3.48: Verify the identity.cos u v cos u v cos2 u sin2 v
 6.6.3.49: Verify the identity. 1cot cotsinsinsin
 6.6.3.50: Verify the identity.1tan tancoscossin
 6.6.3.51: Express in terms of trigonometric functions of u, v, and w. (Hint: ...
 6.6.3.52: Express in terms of trigonometric functions of u, v, and w.
 6.6.3.53: Derive the formula . cot u v cot u cot v 1 cot u cot v
 6.6.3.54: If and are complementary angles, show that
 6.6.3.55: Derive the subtraction formula for the sine function.
 6.6.3.56: Derive the subtraction formula for the tangent function.
 6.6.3.57: If , show that
 6.6.3.58: If , show that
 6.6.3.59: (a) Compare the decimal approximations of both sides of equation (1...
 6.6.3.60: (a) Compare the decimal approximations of both sides of equation (1...
 6.6.3.61: Use an addition or subtraction formula to find the solutions of the...
 6.6.3.62: Use an addition or subtraction formula to find the solutions of the...
 6.6.3.63: Use an addition or subtraction formula to find the solutions of the...
 6.6.3.64: Use an addition or subtraction formula to find the solutions of the...
 6.6.3.65: Use an addition or subtraction formula to find the solutions of the...
 6.6.3.66: Use an addition or subtraction formula to find the solutions of the...
 6.6.3.67: (a) Use the formula from Example 7 to express f in terms of the cos...
 6.6.3.68: (a) Use the formula from Example 7 to express f in terms of the cos...
 6.6.3.69: (a) Use the formula from Example 7 to express f in terms of the cos...
 6.6.3.70: (a) Use the formula from Example 7 to express f in terms of the cos...
 6.6.3.71: For certain applications in electrical engineering, the sum of seve...
 6.6.3.72: For certain applications in electrical engineering, the sum of seve...
 6.6.3.73: Motion of a mass If a mass that is attached to a spring is raised f...
 6.6.3.74: Motion of a mass Refer to Exercise 73. If and , find the initial ve...
 6.6.3.75: Pressure on the eardrum If a tuning fork is struck and then held a ...
 6.6.3.76: Destructive interference Refer to Exercise 75. When two tuning fork...
 6.6.3.77: Constructive interference Refer to Exercise 75. When two tuning for...
 6.6.3.78: Pressure on the eardrum Refer to Exercise 75. If two tuning forks w...
 6.6.3.79: Refer to Exercise 77. Graph the equation for t , and estimate the i...
 6.6.3.80: Refer to Exercise 77. Graph the equation for t , and estimate the i...
 6.6.4.1: Find the exact values of sin 2 , cos 2 , and tan 2 for the given va...
 6.6.4.2: Find the exact values of sin 2 , cos 2 , and tan 2 for the given va...
 6.6.4.3: Find the exact values of sin 2 , cos 2 , and tan 2 for the given va...
 6.6.4.4: Find the exact values of sin 2 , cos 2 , and tan 2 for the given va...
 6.6.4.5: If tan 3 and is acute, find the exact value of sin 2 .
 6.6.4.6: If cot 2 and is acute, find the exact value of cos 2 .
 6.6.4.7: Find the exact values of sin ( 2), cos ( 2), andtan ( 2) for the gi...
 6.6.4.8: Find the exact values of sin ( 2), cos ( 2), andtan ( 2) for the gi...
 6.6.4.9: Find the exact values of sin ( 2), cos ( 2), andtan ( 2) for the gi...
 6.6.4.10: Find the exact values of sin ( 2), cos ( 2), andtan ( 2) for the gi...
 6.6.4.11: Find the exact values of sin ( 2), cos ( 2), andtan ( 2) for the gi...
 6.6.4.12: Find the exact values of sin ( 2), cos ( 2), andtan ( 2) for the gi...
 6.6.4.13: If cos and is in the fourth quadrant, find the exactvalue of tan ( 2).
 6.6.4.14: If sec , what possible values can tan ( 2) have?
 6.6.4.15: Use halfangle formulas to find the exact values.
 6.6.4.16: Use halfangle formulas to find the exact values.
 6.6.4.17: Verify the identity.
 6.6.4.18: Verify the identity.cos2 3x sin2 3x cos 6x
 6.6.4.19: Verify the identity.4 sin x 2cos x 2 2 sinx
 6.6.4.20: Verify the identity.sin2 2 sin2 4 4 sin2
 6.6.4.21: Verify the identity.sin2 x 2sin2 x 2(1 cos x)
 6.6.4.22: Verify the identity.cos2 x 2sin2 x 2(1 cos x)
 6.6.4.23: Verify the identity.sin t cos t2 1 sin 2t
 6.6.4.24: Verify the identity.csc 2u 1 2 csc u sec u
 6.6.4.25: Verify the identity.sin 3u sin u 3 4 sin2 u
 6.6.4.26: Verify the identity.sin 4t 4 sin t cos t 1 2 sin 2 t
 6.6.4.27: Verify the identity.cos 4 8 cos 4 8 cos 2 1
 6.6.4.28: Verify the identity.
 6.6.4.29: Verify the identity.sin4 t 3 8 1 2 cos 2t 1 8 cos 4t
 6.6.4.30: Verify the identity.cos4 x sin4 x cos 2x
 6.6.4.31: Verify the identity.
 6.6.4.32: Verify the identity.
 6.6.4.33: Verify the identity.2 sin2 2t cos 4t 1
 6.6.4.34: Verify the identity.tan cot 2 csc 2
 6.6.4.35: Verify the identity.tan 3u tan u 3 tan2 u 1 3 tan2 u
 6.6.4.36: Verify the identity.1 sin 2v cos 2v 1 sin 2v cos 2v cot v
 6.6.4.37: Verify the identity.tan 2 csc cot
 6.6.4.38: Verify the identity.tan2 2 1 2 cot csc 2 cot2
 6.6.4.39: Express in terms of the cosine function with exponent 1.
 6.6.4.40: Express in terms of the cosine function with exponent 1.cos4 2
 6.6.4.41: Express in terms of the cosine function with exponent 1.
 6.6.4.42: Express in terms of the cosine function with exponent 1.sin4 2
 6.6.4.43: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.44: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.45: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.46: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.47: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.48: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.49: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.50: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.51: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.52: Find the solutions of the equation that are in the interval [0, 2 ).
 6.6.4.53: If , , and , show thatfor , withand
 6.6.4.54: Use Exercise 53 to express in the form .
 6.6.4.55: A graph of for is shown in the figure.(a) Approximate the xinterce...
 6.6.4.56: A graph of for is shown in the figure.(a) Find the xintercepts.(b)...
 6.6.4.57: A graph of for is shown in the figure on the next page.(a) Find the...
 6.6.4.58: A graph of for is shown in the figure. Find the xintercepts. (Hint...
 6.6.4.59: Planning a railroad route Shown in the figure is a proposed railroa...
 6.6.4.60: Projectiles range If a projectile is fired from ground level with a...
 6.6.4.61: Constructing a rain gutter Shown in the figure is a design for a ra...
 6.6.4.62: Designing curbing A highway engineer is designing curbing for a str...
 6.6.4.63: Arterial bifurcation A common form of cardiovascular branching is b...
 6.6.4.64: Heat production in an AC circuit By definition, the average value o...
 6.6.4.65: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.4.66: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.4.67: Graphically solve the trigonometric equation on the indicated inter...
 6.6.4.68: Graphically solve the trigonometric equation on the indicated inter...
 6.6.4.69: Graphically solve the trigonometric equation on the indicated inter...
 6.6.4.70: Graphically solve the trigonometric equation on the indicated inter...
 6.6.4.71: Graphically solve the trigonometric equation on the indicated inter...
 6.6.4.72: Graphically solve the trigonometric equation on the indicated inter...
 6.6.5.1: Express as a sum or difference.
 6.6.5.2: Express as a sum or difference.
 6.6.5.3: Express as a sum or difference.
 6.6.5.4: Express as a sum or difference.
 6.6.5.5: Express as a sum or difference.
 6.6.5.6: Express as a sum or difference.
 6.6.5.7: Express as a sum or difference.
 6.6.5.8: Express as a sum or difference.
 6.6.5.9: Express as a product.
 6.6.5.10: Express as a product.
 6.6.5.11: Express as a product.
 6.6.5.12: Express as a product.
 6.6.5.13: Express as a product.
 6.6.5.14: Express as a product.
 6.6.5.15: Express as a product.
 6.6.5.16: Express as a product.
 6.6.5.17: Verify the identity. sin 4t sin 6t cos 4t cos 6t cot
 6.6.5.18: Verify the identity.sin sin 3 cos cos 3 tan 2
 6.6.5.19: Verify the identity.sin u sin v cos u cos v tan 1 2u v
 6.6.5.20: Verify the identity.sin u sin v cos u cos vcot 1 2u v
 6.6.5.21: Verify the identity.sin u sin v sin u sin vtan 1 2u v tan 1 2u v
 6.6.5.22: Verify the identity.cos u cos v cos u cos vtan 1 2u v tan 1 2u v
 6.6.5.23: Verify the identity.4 cosx cos 2x sin 3x sin 2x sin 4x sin 6x
 6.6.5.24: Verify the identity.cos t cos 4t cos 7t sin t sin 4t sin 7t cot 4t
 6.6.5.25: Express as a sum.
 6.6.5.26: Express as a sum.
 6.6.5.27: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.28: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.29: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.30: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.31: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.32: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.33: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.34: Use sumtoproduct formulas to find the solutions of the equation.
 6.6.5.35: Shown in the figure is a graph of the function f for 0 x 2 . Use a ...
 6.6.5.36: Shown in the figure is a graph of the function f for 0 x 2 . Use a ...
 6.6.5.37: Refer to Exercise 57 of Section 6.4. The graph of the equation has ...
 6.6.5.38: Refer to Exercise 58 of Section 6.4. The xcoordinates of the turni...
 6.6.5.39: Vibration of a violin string Mathematical analysis of a vibrating v...
 6.6.5.40: Pressure on the eardrum If two tuning forks are struck simultaneous...
 6.6.5.41: Graph f on the interval [ , ]. (a) Estimate the xintercepts. (b) U...
 6.6.5.42: Graph f on the interval [ , ]. (a) Estimate the xintercepts. (b) U...
 6.6.5.43: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.5.44: Use the graph of f to find the simplest expression g(x) such that t...
 6.6.5.45: Find the exact value of the expression whenever it is defined.
 6.6.6.1: Find the exact value of the expression whenever it is defined.
 6.6.6.2: Find the exact value of the expression whenever it is defined.
 6.6.6.3: Find the exact value of the expression whenever it is defined.
 6.6.6.4: Find the exact value of the expression whenever it is defined.
 6.6.6.5: Find the exact value of the expression whenever it is defined.
 6.6.6.6: Find the exact value of the expression whenever it is defined.
 6.6.6.7: Find the exact value of the expression whenever it is defined.
 6.6.6.8: Find the exact value of the expression whenever it is defined.
 6.6.6.9: Find the exact value of the expression whenever it is defined.
 6.6.6.10: Find the exact value of the expression whenever it is defined.
 6.6.6.11: Find the exact value of the expression whenever it is defined.
 6.6.6.12: Find the exact value of the expression whenever it is defined.
 6.6.6.13: Find the exact value of the expression whenever it is defined.
 6.6.6.14: Find the exact value of the expression whenever it is defined.
 6.6.6.15: Find the exact value of the expression whenever it is defined.
 6.6.6.16: Find the exact value of the expression whenever it is defined.
 6.6.6.17: Find the exact value of the expression whenever it is defined.
 6.6.6.18: Find the exact value of the expression whenever it is defined.
 6.6.6.19: Find the exact value of the expression whenever it is defined.
 6.6.6.20: Find the exact value of the expression whenever it is defined.
 6.6.6.21: Find the exact value of the expression whenever it is defined.
 6.6.6.22: Find the exact value of the expression whenever it is defined.
 6.6.6.23: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.24: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.25: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.26: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.27: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.28: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.29: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.30: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.31: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.32: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.33: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.34: Write the expression as an algebraic expression in x for x > 0.
 6.6.6.35: Complete the statements. (a) As , ___ (b) As , ___ (c) As , ___
 6.6.6.36: Complete the statements. (a) As , ___ (b) As , ___ (c) As , ___
 6.6.6.37: Sketch the graph of the equation.
 6.6.6.38: Sketch the graph of the equation.
 6.6.6.39: Sketch the graph of the equation.
 6.6.6.40: Sketch the graph of the equation.
 6.6.6.41: Sketch the graph of the equation.
 6.6.6.42: Sketch the graph of the equation.
 6.6.6.43: Sketch the graph of the equation.
 6.6.6.44: Sketch the graph of the equation.
 6.6.6.45: Sketch the graph of the equation.
 6.6.6.46: Sketch the graph of the equation.
 6.6.6.47: Sketch the graph of the equation.
 6.6.6.48: Sketch the graph of the equation.
 6.6.6.49: Sketch the graph of the equation.
 6.6.6.50: Sketch the graph of the equation.
 6.6.6.51: The given equation has the form y f(x). (a) Find the domain of f. (...
 6.6.6.52: The given equation has the form y f(x). (a) Find the domain of f. (...
 6.6.6.53: The given equation has the form y f(x). (a) Find the domain of f. (...
 6.6.6.54: The given equation has the form y f(x). (a) Find the domain of f. (...
 6.6.6.55: Solve the equation for x in terms of y if x is restricted to the gi...
 6.6.6.56: Solve the equation for x in terms of y if x is restricted to the gi...
 6.6.6.57: Solve the equation for x in terms of y if x is restricted to the gi...
 6.6.6.58: Solve the equation for x in terms of y if x is restricted to the gi...
 6.6.6.59: Solve the equation for x in terms of y if 0 < x < and 0 < y < .
 6.6.6.60: Solve the equation for x in terms of y if 0 < x < and 0 < y < .
 6.6.6.61: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.62: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.63: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.64: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.65: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.66: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.67: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.68: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.69: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.70: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.71: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.72: Use inverse trigonometric functions to find the solutions of the eq...
 6.6.6.73: If an earthquake has a total horizontal displacement of S meters al...
 6.6.6.74: If an earthquake has a total horizontal displacement of S meters al...
 6.6.6.75: A golfers drive A golfer, centered in a 30yardwide straight fairw...
 6.6.6.76: Placing a wooden brace A 14foot piece of lumber is to be placed as...
 6.6.6.77: Tracking a sailboat As shown in the figure, a sailboat is following...
 6.6.6.78: Calculating viewing angles An art critic whose eye level is 6 feet ...
 6.6.6.79: Verify the identity.sin1 x tan1 x 1 x2
 6.6.6.80: Verify the identity.
 6.6.6.81: Verify the identity.arcsin x arcsin x
 6.6.6.82: Verify the identity.arccos x arccos x
 6.6.6.83: Verify the identity.
 6.6.6.84: Verify the identity.
 6.6.6.85: Graph f, and determine its domain and range. fx 2 sin1 x 1 cos1 1 2x
 6.6.6.86: Graph f, and determine its domain and range.fx 1 2 tan1 1 2x 3 tan ...
 6.6.6.87: Use a graph to estimate the solutions of the equation.sin1 2x tan1 1 x
 6.6.6.88: Use a graph to estimate the solutions of the equation. cos1 x 1 5 2...
 6.6.6.89: Designing a solar collector In designing a collector for solar powe...
 6.6.6.90: Designing a solar collector The altitude of the sun is the angle th...
 6.6.6.91: Many calculators have viewing screens that are wider than they are ...
 6.6.6.92: Many calculators have viewing screens that are wider than they are ...
 6.6.6.93: Many calculators have viewing screens that are wider than they are ...
 6.6.6.94: Many calculators have viewing screens that are wider than they are ...
 6.6.7.1: Verify the identity.cot2 x 11 cos2 x 1
 6.6.7.2: Verify the identity.cos sintan sec
 6.6.7.3: Verify the identity.sec2 1 cottansin cos sin
 6.6.7.4: Verify the identity.tan x cot x2 sec2 x csc2 x
 6.6.7.5: Verify the identity.1 1 sin t sec t tan t sec t
 6.6.7.6: Verify the identity.sin cos tan tan1 tantan
 6.6.7.7: Verify the identity.
 6.6.7.8: Verify the identity.v 21 sec v 2 sec v
 6.6.7.9: Verify the identity.tan3 cot3tan2 csc2 tan cot
 6.6.7.10: Verify the identity.sin u sin v csc u csc v1 sin u sin v 1 csc u csc v
 6.6.7.11: Verify the identity.in2 x tan4 x3csc3 x cot6 x2 1
 6.6.7.12: Verify the identity.cos 1 tansin 1 cot cos sin
 6.6.7.13: Verify the identity.cos t sec t tan t 1 sin t
 6.6.7.14: Verify the identity.cot t csc t sin t1 1 cos t
 6.6.7.15: Verify the identity.1 cos t 1 cos t1 cos tsin t
 6.6.7.16: Verify the identity.
 6.6.7.17: Verify the identity.
 6.6.7.18: Verify the identity.
 6.6.7.19: Verify the identity.
 6.6.7.20: Verify the identity.tan 1 2 csc cot
 6.6.7.21: Verify the identity.in 8 8 sincos 1 2 sin 2 1 8 sin2cos2
 6.6.7.22: Verify the identity.arctan x 1 2arctan 2x 1 x2, 1x1
 6.6.7.23: Find the solutions of the equation that are in the interval [0, 22 ...
 6.6.7.24: Find the solutions of the equation that are in the interval [0, 32 ...
 6.6.7.25: Find the solutions of the equation that are in the interval [0, 4
 6.6.7.26: Find the solutions of the equation that are in the interval [0, 5cs...
 6.6.7.27: Find the solutions of the equation that are in the interval [0, 62 ...
 6.6.7.28: Find the solutions of the equation that are in the interval [0, 7
 6.6.7.29: Find the solutions of the equation that are in the interval [0, 8
 6.6.7.30: Find the solutions of the equation that are in the interval [0, 9 c...
 6.6.7.31: Find the solutions of the equation that are in the interval [0, 10 ...
 6.6.7.32: Find the solutions of the equation that are in the interval [0, 11 ...
 6.6.7.33: Find the solutions of the equation that are in the interval [0, 12 ...
 6.6.7.34: Find the solutions of the equation that are in the interval [0, 13
 6.6.7.35: Find the solutions of the equation that are in the interval [0, 14
 6.6.7.36: Find the solutions of the equation that are in the interval [0, 15
 6.6.7.37: Find the solutions of the equation that are in the interval [0, 16
 6.6.7.38: Find the solutions of the equation that are in the interval [0, 17
 6.6.7.39: Find the solutions of the equation that are in the interval [0, 18
 6.6.7.40: Find the solutions of the equation that are in the interval [0, 19
 6.6.7.41: Find the exact value.
 6.6.7.42: Find the exact value. tan 285
 6.6.7.43: Find the exact value.
 6.6.7.44: Find the exact value. csc 8
 6.6.7.45: If and are acute angles such that and , find the exact value.
 6.6.7.46: If and are acute angles such that and , find the exact value.
 6.6.7.47: If and are acute angles such that and , find the exact value.
 6.6.7.48: If and are acute angles such that and , find the exact value.
 6.6.7.49: If and are acute angles such that and , find the exact value.
 6.6.7.50: If and are acute angles such that and , find the exact value.
 6.6.7.51: If and are acute angles such that and , find the exact value.
 6.6.7.52: If and are acute angles such that and , find the exact value.
 6.6.7.53: If and are acute angles such that and , find the exact value.
 6.6.7.54: If and are acute angles such that and , find the exact value.
 6.6.7.55: If and are acute angles such that and , find the exact value.
 6.6.7.56: If and are acute angles such that and , find the exact value.
 6.6.7.57: If and are acute angles such that and , find the exact value.
 6.6.7.58: If and are acute angles such that and , find the exact value.
 6.6.7.59: Express as a sum or difference: (a) (b)(c) (d)
 6.6.7.60: Express as a product: (a) (b)(c) (d)
 6.6.7.61: Find the exact value of the expression whenever it is defined.
 6.6.7.62: Find the exact value of the expression whenever it is defined.
 6.6.7.63: Find the exact value of the expression whenever it is defined.
 6.6.7.64: Find the exact value of the expression whenever it is defined.
 6.6.7.65: Find the exact value of the expression whenever it is defined.
 6.6.7.66: Find the exact value of the expression whenever it is defined.
 6.6.7.67: Find the exact value of the expression whenever it is defined.
 6.6.7.68: Find the exact value of the expression whenever it is defined.
 6.6.7.69: Find the exact value of the expression whenever it is defined.
 6.6.7.70: Find the exact value of the expression whenever it is defined.
 6.6.7.71: Find the exact value of the expression whenever it is defined.
 6.6.7.72: Find the exact value of the expression whenever it is defined.
 6.6.7.73: Find the exact value of the expression whenever it is defined.
 6.6.7.74: Find the exact value of the expression whenever it is defined.
 6.6.7.75: Find the exact value of the expression whenever it is defined.
 6.6.7.76: Find the exact value of the expression whenever it is defined.
 6.6.7.77: Sketch the graph of the equation.
 6.6.7.78: Sketch the graph of the equation.
 6.6.7.79: Sketch the graph of the equation.
 6.6.7.80: Sketch the graph of the equation.
 6.6.7.81: Express in terms of trigonometric functions of , , and .
 6.6.7.82: Force of a foot When an individual is walking, the magnitude F of t...
 6.6.7.83: Shown in the figure is a graph of the equationThe xcoordinates of ...
 6.6.7.84: Visual distinction The human eye can distinguish between two distan...
 6.6.7.85: Satellites A satellite S circles a planet at a distance d miles fro...
 6.6.7.86: Urban canyons Because of the tall buildings and relatively narrow s...
 6.6.8.1: Verify the following identity:(Hint: At some point, consider a spec...
 6.6.8.2: Refer to Example 6 of Section 6.1. Suppose , and rewrite the conclu...
 6.6.8.3: How many solutions does the following equation have on ? Find the l...
 6.6.8.4: Graph the difference quotient for and , 0.1, and 0.001 on the viewi...
 6.6.8.5: There are several interesting exact relationships between and inver...
 6.6.8.6: Shown in the figure is a function called a sawtooth function. (a) D...
 6.6.8.7: Verify the following identity: sin4 (x2) cos4 (x2) sin4 (x2) cos4 (...
 6.6.9.1: Verify the identity:
 6.6.9.2: Verify the identity:
 6.6.9.3: Show that is not an identity.
 6.6.9.4: Make the trigonometric substitution in , where and a0, and use fund...
 6.6.9.5: Find all solutions of the equation .
 6.6.9.6: Find an expression for the xcoordinates of the highest points of t...
 6.6.9.7: Find all xintercepts
 6.6.9.8: Find all solutions of the equation .
 6.6.9.9: Use the fact that to find an exact value for .
 6.6.9.10: If and tan 0, find the exact value of .
 6.6.9.11: If and are secondquadrant angles such that and , find .
 6.6.9.12: Verify the reduction formula:
 6.6.9.13: Use an addition or subtraction formula to find the solutions of the...
 6.6.9.14: Given that and , find the exact values of , ,and .
 6.6.9.15: Given that and 900, find the exact values of ,, and .
 6.6.9.16: Verify the identity:
 6.6.9.17: Find the solutions of the equation that are in the interval .
 6.6.9.18: Express 4 cos x cos 7x as a simplified sum or difference.
 6.6.9.19: Express cos x cos 7x as a simplified product.
 6.6.9.20: Verify the identity:
 6.6.9.21: Find the solutions of the equation sin 7x sin x 0.
 6.6.9.22: Find the exact value of .
 6.6.9.23: Find the values of for which .
 6.6.9.24: Find the exact value of .
 6.6.9.25: Write as an algebraic expression in a and c for positive a and c.
 6.6.9.26: Complete the statement: As , ____.
 6.6.9.27: Solve for x in terms of y.
 6.6.9.28: Find the exact solutions and twodecimalplace approximations of th...
Solutions for Chapter 6: ANALYTIC TRIGONOMETRY
Full solutions for Precalculus: Functions and Graphs  12th Edition
ISBN: 9780840068576
Solutions for Chapter 6: ANALYTIC TRIGONOMETRY
Get Full SolutionsPrecalculus: Functions and Graphs was written by and is associated to the ISBN: 9780840068576. Chapter 6: ANALYTIC TRIGONOMETRY includes 599 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 599 problems in chapter 6: ANALYTIC TRIGONOMETRY have been answered, more than 19118 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus: Functions and Graphs, edition: 12.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Bar chart
A rectangular graphical display of categorical data.

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Cubic
A degree 3 polynomial function

Directed distance
See Polar coordinates.

Divisor of a polynomial
See Division algorithm for polynomials.

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

Leading coefficient
See Polynomial function in x

Line graph
A graph of data in which consecutive data points are connected by line segments

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Normal curve
The graph of ƒ(x) = ex2/2

Partial sums
See Sequence of partial sums.

Perpendicular lines
Two lines that are at right angles to each other

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Range (in statistics)
The difference between the greatest and least values in a data set.

Reciprocal function
The function ƒ(x) = 1x

Reciprocal of a real number
See Multiplicative inverse of a real number.

Variable
A letter that represents an unspecified number.

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k

Vertical stretch or shrink
See Stretch, Shrink.