 8.1: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.1: Use Figure 8.12 to find the following exactly: (a) tan (b) sin (c) ...
 8.8.2.1: In Exercises 12, solve for . 6 10018
 8.8.3.1: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.2: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.2: Using Figure 8.13, find exactly: (a) sin (b) sin (c) cos (d) cos (e...
 8.8.2.2: In Exercises 12, solve for . 352
 8.8.3.2: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.3: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.3: In Exercises 36, find (a) sin (b) cos 1024 2
 8.8.2.3: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.3: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.4: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.4: In Exercises 36, find (a) sin (b) cos 69117
 8.8.2.4: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.4: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.5: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.5: In Exercises 36, find (a) sin (b) cos 0.10.2
 8.8.2.5: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.5: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.6: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.6: In Exercises 36, find (a) sin (b) cos 23
 8.8.2.6: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.6: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.8.3.7: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.7: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.7: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.7: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.8: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.8: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.8: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.8: Find all sides and angles of the triangles in 38. (Sides and angles...
 8.8.3.9: In Exercises 19, in which quadrant is a point with the polar coordi...
 8.9: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.9: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.9: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.10: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.10: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.10: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.10: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.11: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.11: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.11: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.11: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.12: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.12: Are the statements in 112 true or false? Give an explanation for yo...
 8.8.1.12: In Exercises 712, one of the sides , and of the triangle in Figure ...
 8.8.2.12: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.13: In Exercises 1013 mark the point on the plane. In which range, 0 t...
 8.13: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.13: For Exercises 1318, find , an angle in a right triangle. sin = 0.876
 8.8.2.13: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.14: Convert the Cartesian coordinates in 1418 to polar coordinates. (1, 1)
 8.14: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.14: For Exercises 1318, find , an angle in a right triangle. cos = 0.016
 8.8.2.14: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.15: Convert the Cartesian coordinates in 1418 to polar coordinates. (1, 0)
 8.15: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.15: For Exercises 1318, find , an angle in a right triangle. tan = 0.123
 8.8.2.15: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.16: Convert the Cartesian coordinates in 1418 to polar coordinates. (6,2)
 8.16: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.16: For Exercises 1318, find , an angle in a right triangle. tan = 54.169
 8.8.2.16: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.17: Convert the Cartesian coordinates in 1418 to polar coordinates. (3, 1)
 8.17: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.17: For Exercises 1318, find , an angle in a right triangle. sin = 0.999
 8.8.2.17: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.18: Convert the Cartesian coordinates in 1418 to polar coordinates. (3,...
 8.18: Are the statements in 1318 true or false? Give an explanation for y...
 8.8.1.18: For Exercises 1318, find , an angle in a right triangle. cos = 0.999
 8.8.2.18: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.19: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.19: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.19: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.19: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.20: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.20: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.20: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.20: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.21: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.21: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.21: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.21: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.22: Convert the polar coordinates in Exercises 1922 to Cartesian coordi...
 8.22: Convert each of the polar coordinates in Exercises 1922 to Cartesia...
 8.8.1.22: In Exercises 1922, find the missing sides and angles in the right t...
 8.8.2.22: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.23: Convert the equations in 2326 to rectangular coordinates. = 2
 8.23: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.23: Use Figure 8.15 to explain why, for between 0 and 90, the unit circ...
 8.8.2.23: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.24: Convert the equations in 2326 to rectangular coordinates. = 6 cos
 8.24: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.24: Using the definition of the trigonometric functions in terms of the...
 8.8.2.24: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.25: Convert the equations in 2326 to rectangular coordinates. = 4
 8.25: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.25: Figure 8.16 shows a 454590 right triangle with side and hypotenus...
 8.8.2.25: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.26: Convert the equations in 2326 to rectangular coordinates. tan = cos 2
 8.26: Find all sides and angles of the triangles in Exercises 2326. (Not ...
 8.8.1.26: Figure 8.17 shows an equilateral triangle with side 2 and altitude ...
 8.8.2.26: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.27: Convert the equations in 2730 to polar coordinates. Express your an...
 8.27: You have been asked to build a ramp for Dans Daredevil Motorcycle J...
 8.8.1.27: The top of a 200foot vertical tower is to be anchored by cables th...
 8.8.2.27: In Exercises 927, use Figure 8.34 to find the missing sides, , , , ...
 8.8.3.28: Convert the equations in 2730 to polar coordinates. Express your an...
 8.28: Find the value of the angle in Figure 8.63. 52 25 63 Figure 8.63
 8.8.1.28: A surveyor must measure the distance between the two banks of a str...
 8.8.2.28: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.29: Convert the equations in 2730 to polar coordinates. Express your an...
 8.29: A ship spots a second ship to its east at a distance of four miles....
 8.8.1.29: A search and rescue volunteer leaves a rendezvous point in the Ariz...
 8.8.2.29: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.30: Convert the equations in 2730 to polar coordinates. Express your an...
 8.30: The ground crew for a hot air balloon is positioned 200 meters from...
 8.8.1.30: In 3033, a line passing through the origin and the given point form...
 8.8.2.30: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.31: For 3138, the origin is at the center of a clock, with the positive...
 8.31: A UFO is first sighted at a point 1 due east from an observer at an...
 8.8.1.31: In 3033, a line passing through the origin and the given point form...
 8.8.2.31: Find all sides and angles of the triangles in Exercises 2831. Sketc...
 8.8.3.32: For 3138, the origin is at the center of a clock, with the positive...
 8.32: A kite flier wondered how high her kite was flying. She used a prot...
 8.8.1.32: In 3033, a line passing through the origin and the given point form...
 8.8.2.32: (a) Find an expression for sin in Figure 8.35 and sin in Figure 8.3...
 8.8.3.33: For 3138, the origin is at the center of a clock, with the positive...
 8.33: Hampton is a small town on a straight stretch of coastline running ...
 8.8.1.33: In 3033, a line passing through the origin and the given point form...
 8.8.2.33: In Figure 8.37: (a) Find sin (b) Solve for (c) Find the area of the...
 8.8.3.34: For 3138, the origin is at the center of a clock, with the positive...
 8.34: For each of the following expressions, find a line segment in Figur...
 8.8.1.34: A 240ft tree casts a 130foot shadow on horizontal ground. A girl ...
 8.8.2.34: Two fire stations are located 56.7 miles apart, at points and . The...
 8.8.3.35: For 3138, the origin is at the center of a clock, with the positive...
 8.35: Find tan exactly if sin = 35, and is in the fourth quadrant.
 8.8.1.35: A plane is flying at an elevation of 35,000 feet when the Gateway A...
 8.8.2.35: To measure the height of the Eiffel Tower in Paris, a person stands...
 8.8.3.36: For 3138, the origin is at the center of a clock, with the positive...
 8.36: Find the radian value of in Figure 8.68. 0.83 1 Figure 8.68
 8.8.1.36: A bridge over a river was damaged in an earthquake and you are call...
 8.8.2.36: Two airplanes leave Kennedy airport in New York at 11 am. The air t...
 8.8.3.37: For 3138, the origin is at the center of a clock, with the positive...
 8.37: (a) Explain why = 2 cos and ( 1)2 + 2 = 1 are equations for the sam...
 8.8.1.37: You want to build a wheelchair ramp leading up to your house. Your ...
 8.8.2.37: A parcel of land is in the shape of an isosceles triangle. The base...
 8.8.3.38: For 3138, the origin is at the center of a clock, with the positive...
 8.8.1.38: The pitch of a roof is the slope of a roof expressed as the ratio o...
 8.8.2.38: In video games, images are drawn on the screen using coordinates. ...
 8.8.3.39: In 3941, give inequalities for and that describe the following regi...
 8.8.1.39: Find approximately the acute angle formed by the line = 2 + 5 and t...
 8.8.2.39: A computergenerated image begins at screen coordinates (5, 3). The...
 8.8.3.40: In 3941, give inequalities for and that describe the following regi...
 8.8.1.40: (a) Find expressions in terms of , , and for the sine, cosine, and ...
 8.8.2.40: Derive the Law of Cosines assuming the angle is obtuse, as in Figur...
 8.8.3.41: In 3941, give inequalities for and that describe the following regi...
 8.8.1.41: Knowing the height of the Columbia Tower in Seattle, determine the ...
 8.8.2.41: Use Figure 8.39 to show that sin = sin . Figure 8.39
 8.8.3.42: (a) Make a table of values for the equation = 1 sin . Include = 0, ...
 8.8.1.42: A tree 50 feet tall casts a shadow 60 feet long. Find the angle of ...
 8.8.2.42: In baseball, the four bases form a square. The pitcher stands near ...
 8.8.3.43: Graph the equation = 1 sin(), for = 1, 2, 3, 4. What is the relatio...
 8.8.1.43: A staircase is to rise 17.3 feet over a horizontal distance of 10 f...
 8.8.2.43: A park director wants to build a bridge across a river to a bird sa...
 8.8.3.44: Graph the equation = 1 sin , with 0 , for = 2, 3, 4. What is the re...
 8.8.1.44: (a) In the right triangle in Figure 8.23, angle = 30 and = 2 3. Fin...
 8.8.2.44: To estimate the width of an archaeological mound, archaeologists pl...
 8.8.3.45: Graph the equation =1 sin , for = 2, 3, 4. What is the relationship...
 8.8.1.45: To check the calibration of their transit (an instrument to measure...
 8.8.2.45: Every triangle has three sides and three angles. Make a chart showi...
 8.8.3.46: Graph the equation = 1cos . Describe its relationship to = 1 sin .
 8.8.1.46: A ladder 3 meters long leans against a house, making an angle with ...
 8.8.2.46: The telephone company needs to run a wire from the telephone pole a...
 8.8.3.47: Give inequalities that describe the flat surface of a washer that i...
 8.8.1.47: You are parasailing on a rope that is 125 feet long behind a boat. ...
 8.8.2.47: A buyer is interested in purchasing the triangular lot with vertice...
 8.8.3.48: Graph the equation = 1 sin(2) for 0 2. There are two loops. For eac...
 8.8.2.48: Solve the following triangles for and . 40 8 7 (a) Figure 8.45 40 8...
 8.8.3.49: A slice of pizza is one eighth of a circle of radius 1 foot. The sl...
 8.8.2.49: A triangle has angles 23, 5, and 215. The length of the side opposi...
 8.8.3.50: A radio tower located on the coast can be configured to transmit mo...
 8.8.3.51: A superdirectional microphone, also called shotgun microphone,6 is...
Solutions for Chapter 8: Functions Modeling Change: A Preparation for Calculus 5th Edition
Full solutions for Functions Modeling Change: A Preparation for Calculus  5th Edition
ISBN: 9781118583197
Solutions for Chapter 8
Get Full SolutionsChapter 8 includes 184 full stepbystep solutions. Since 184 problems in chapter 8 have been answered, more than 10327 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9781118583197. This textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus, edition: 5.

Addition property of inequality
If u < v , then u + w < v + w

Difference identity
An identity involving a trigonometric function of u  v

Directed distance
See Polar coordinates.

Equation
A statement of equality between two expressions.

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Frequency table (in statistics)
A table showing frequencies.

Identity function
The function ƒ(x) = x.

Initial point
See Arrow.

Positive numbers
Real numbers shown to the right of the origin on a number line.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Remainder polynomial
See Division algorithm for polynomials.

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the righthand end point of each subinterval.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Slopeintercept form (of a line)
y = mx + b

Solve an equation or inequality
To find all solutions of the equation or inequality

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.