 9.9.2.1: The difference formula for the sine function is sin(A  B) = __ . (...
 9.9.4.1: The area of a triangle whose base is b and whose height is h is __ ...
 9.9.5.1: The amplitude A and period T of f(x) = 5 sin (4x) are __ and __ . (...
 9.9.3.1: Write the formula for the distance d from PI = (XI, YI) to P2 = (X2...
 9.9.1.1: In a right triangle, if the length of the hypotenuse is 5 and the l...
 9.1: In 14, solve each triangle. 10 Aa
 9.2: In 14, solve each triangle. n o b c 35 B5
 9.9.2.2: If e is an acute angle, solve the equation cos e = V;. (pp. 649653)
 9.9.4.2: If three sides of a triangle are given, ___ Formula is used to find...
 9.9.5.2: The motion of an object obeys the equation d = 4 cos(6t). Such moti...
 9.9.3.2: If () IS an acute angle, solve the equatIon cos () = . (pp. 649653)
 9.9.1.2: True or False sin 52 = cos 48. (pp. 523525)
 9.3: In 14, solve each triangle. 2 a
 9.9.2.3: The two triangles shown are similar. Find the missing length. (pp. ...
 9.9.4.3: True or False No formula exists for finding the area of a triangle ...
 9.9.5.3: When a mass hanging from a spring is pulled down and then released,...
 9.9.3.3: If three sides of a triangle are given, the Law of ____ is used to ...
 9.9.1.3: If e is an acute angle, solve the equation tan e = . Express your a...
 9.4: In 14, solve each triangle. 13
 9.9.2.4: If none of the angles of a triangle is a right angle, the triangle ...
 9.9.4.4: True or False Given two sides and the included angle, there is a fo...
 9.9.5.4: True or False If the distance d of an object from its rest position...
 9.9.3.4: If one side and two angles of a triangle are given, the Law of ____...
 9.9.1.4: If e is an acute angle, solve the equation sin e = . (pp. 649653)
 9.5: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.5: For a triangle with sides a, b, c and opposite angles A, B, e, the ...
 9.9.4.5: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.5: In 58, an object attached to a coiled spring is pulled down a dist...
 9.9.3.5: If two sides and the included angle of a triangle are given, the La...
 9.9.1.5: True or False In a right triangle, one of the angles is 90 and the ...
 9.6: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.6: True or False An oblique triangle in which two sides and an angle a...
 9.9.4.6: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.6: In 58, an object attached to a coiled spring is pulled down a dist...
 9.9.3.6: True or False Given only the three sides of a triangle, there is in...
 9.9.1.6: In navigation or surveying, the __ from a point to a point P equals...
 9.7: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.7: True or False The sum of the angles of any triangle equals 180.
 9.9.4.7: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.7: In 58, an object attached to a coiled spring is pulled down a dist...
 9.9.3.7: True or False Given two sides and the included angle, the first thi...
 9.9.1.7: True or False In a right triangle, if two sides are known, we can s...
 9.8: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.8: True or False The ambiguous case refers to the fact that, when two ...
 9.9.4.8: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.8: In 58, an object attached to a coiled spring is pulled down a dist...
 9.9.3.8: True or False A special case of the Law of Cosines is the Pythagore...
 9.9.1.8: True or False In a right triangle, if we know the two acute angles,...
 9.9: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.9: In 916, solve each triangle. A. 5
 9.9.4.9: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.9: Rework under the same conditions except that, at time t = 0, the ob...
 9.9.3.9: In 916, solve each triangle. 2 b4
 9.9.1.9: In 922, use the right triangle shown below. Then, using the given ...
 9.10: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.10: In 916, solve each triangle. 4
 9.9.4.10: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.10: Rework under the same conditions except that, at time t = 0, the ob...
 9.9.3.10: In 916, solve each triangle. B 30 4
 9.9.1.10: In 922, use the right triangle shown below. Then, using the given ...
 9.11: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.11: In 916, solve each triangle. B c
 9.9.4.11: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.11: Rework under the same conditions except that, at time t = 0, the ob...
 9.9.3.11: In 916, solve each triangle.
 9.9.1.11: In 922, use the right triangle shown below. Then, using the given ...
 9.12: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.12: In 916, solve each triangle. 10 A c
 9.9.4.12: In 512, find the area of each triangle. Round answers to two decim...
 9.9.5.12: Rework under the same conditions except that, at time t = 0, the ob...
 9.9.3.12: In 916, solve each triangle. 20 A5
 9.9.1.12: In 922, use the right triangle shown below. Then, using the given ...
 9.13: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.13: In 916, solve each triangle. c
 9.9.4.13: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.13: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.13: In 916, solve each triangle. 5A 8
 9.9.1.13: In 922, use the right triangle shown below. Then, using the given ...
 9.14: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.14: In 916, solve each triangle. 5 5 b :
 9.9.4.14: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.14: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.14: In 916, solve each triangle. d B A4
 9.9.1.14: In 922, use the right triangle shown below. Then, using the given ...
 9.15: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.15: In 916, solve each triangle. c
 9.9.4.15: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.15: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.15: In 916, solve each triangle. 4
 9.9.1.15: In 922, use the right triangle shown below. Then, using the given ...
 9.16: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.16: In 916, solve each triangle. c
 9.9.4.16: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.16: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.16: In 916, solve each triangle. 4
 9.9.1.16: In 922, use the right triangle shown below. Then, using the given ...
 9.17: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.17: In 1724, solve each triangle. A = 40, B = 20, a = 2
 9.9.4.17: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.17: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.17: In 1732, solve each triangle. a = 3, b = 4, C = 40
 9.9.1.17: In 922, use the right triangle shown below. Then, using the given ...
 9.18: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.18: In 1724, solve each triangle. A = 50, e = 20, a = 3
 9.9.4.18: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.18: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.18: In 1732, solve each triangle. a = 2, c = 1, B = 10
 9.9.1.18: In 922, use the right triangle shown below. Then, using the given ...
 9.19: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.19: In 1724, solve each triangle. B = 70, e = 10, b = 5
 9.9.4.19: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.19: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.19: In 1732, solve each triangle. b = 1, C = 3, A = 80
 9.9.1.19: In 922, use the right triangle shown below. Then, using the given ...
 9.20: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.20: In 1724, solve each triangle. A = 70, B = 60, c = 4
 9.9.4.20: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.20: In 1320, the displacement d (in meters) of an object at time t (in...
 9.9.3.20: In 1732, solve each triangle. a = 6, b = 4, C = 60
 9.9.1.20: In 922, use the right triangle shown below. Then, using the given ...
 9.21: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.21: In 1724, solve each triangle. A = 1 10, e = 30, c = 3
 9.9.4.21: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.21: In 2124, graph each damped vibration curve for 0 :S t :S 27 1. d(t...
 9.9.3.21: In 1732, solve each triangle. a = 3, c = 2, B = 110
 9.9.1.21: In 922, use the right triangle shown below. Then, using the given ...
 9.22: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.22: In 1724, solve each triangle. B = 10, e = 100, b = 2
 9.9.4.22: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.22: In 2124, graph each damped vibration curve for 0 :S t :S 27 1. d(t...
 9.9.3.22: In 1732, solve each triangle. b = 4, C = 1, A = 120
 9.9.1.22: In 922, use the right triangle shown below. Then, using the given ...
 9.23: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.23: In 1724, solve each triangle. A = 40, B = 40, c = 2
 9.9.4.23: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.23: In 2124, graph each damped vibration curve for 0 :S t :S 27 1. del...
 9.9.3.23: In 1732, solve each triangle. a = 2, b = 2, C = 50
 9.9.1.23: Geometry The hypotenuse of a right triangle is 5 inches. If one leg...
 9.24: In 524, find the remaining angle(s) and side(s) of each triangle, ...
 9.9.2.24: In 1724, solve each triangle. B = 20, e = 70, a = 1
 9.9.4.24: In 1324, find the area of each triangle. Round answers to two deci...
 9.9.5.24: In 2124, graph each damped vibration curve for 0 :S t :S 27 1. d(t...
 9.9.3.24: In 1732, solve each triangle. a = 3, c = 2, B = 90
 9.9.1.24: Geometry The hypotenuse of a right triangle is 3 feet. If one leg i...
 9.25: In 2534, find the area of each triangle. a = 2, b = 3, C = 40
 9.9.2.25: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.25: Area of an ASA Triangle If two angles and the included side are giv...
 9.9.5.25: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.25: In 1732, solve each triangle. a = 1 2, b = 13, C = 5
 9.9.1.25: Finding the Angle of Elevation of the Sun At 10 AM on April 26, 200...
 9.26: In 2534, find the area of each triangle. b = 5, c = 5, A = 20
 9.9.2.26: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.26: Area of a Triangle Prove the two other forms of the formula given i...
 9.9.5.26: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.26: In 1732, solve each triangle. a = 4, b = 5, c = 3
 9.9.1.26: Directing a Laser Beam A laser beam is to be directed through a sma...
 9.27: In 2534, find the area of each triangle. b = 4, C = 10, A = 70
 9.9.2.27: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.27: In 2732, use the results of or 26 to find the area of each triangl...
 9.9.5.27: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.27: In 1732, solve each triangle. a = 2, b = 2, c = 2
 9.9.1.27: Finding the Speed of a Truck A state trooper is hidden 30 feet from...
 9.28: In 2534, find the area of each triangle. a = 2, b = 1, C = 100
 9.9.2.28: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.28: In 2732, use the results of or 26 to find the area of each triangl...
 9.9.5.28: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.28: In 1732, solve each triangle. a = 3, b = 3, c = 2
 9.9.1.28: Security A security camera in a neighborhood bank is mounted on a w...
 9.29: In 2534, find the area of each triangle. a = 4, b = 3, c = 5
 9.9.2.29: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.29: In 2732, use the results of or 26 to find the area of each triangl...
 9.9.5.29: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.29: In 1732, solve each triangle. a = 5, b = 8, c = 9
 9.9.1.29: Finding the Bearing of an Aircraft A DC9 aircraft leaves Midway Ai...
 9.30: In 2534, find the area of each triangle. a = 10, b = 7, C = 8
 9.9.2.30: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.30: In 2732, use the results of or 26 to find the area of each triangl...
 9.9.5.30: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.30: In 1732, solve each triangle. a = 4, b = 3, c = 6
 9.9.1.30: Finding the Bearing of a Ship A ship leaves the port of Miami with ...
 9.31: In 2534, find the area of each triangle. a = 4, b = 2, C = 5
 9.9.2.31: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.31: In 2732, use the results of or 26 to find the area of each triangl...
 9.9.5.31: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.31: In 1732, solve each triangle. a = 10, b = 8, c = 5
 9.9.1.31: Niagara Falls Incline Railway Situated between Portage Road and the...
 9.32: In 2534, find the area of each triangle. a = 3, b = 2, C = 2
 9.9.2.32: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.32: In 2732, use the results of or 26 to find the area of each triangl...
 9.9.5.32: In 2532, use the method of adding ycoordinates to graph each func...
 9.9.3.32: In 1732, solve each triangle. a = 9, b = 7, c = 10
 9.9.1.32: Sears Tower The Sears Tower in Chicago is the third tallest buildin...
 9.33: In 2534, find the area of each triangle. A = 50, B = 30, a = 1
 9.9.2.33: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.33: Area of a Segment Find the area of the segment (shaded in blue in t...
 9.9.5.33: In 3338, an object of mass m (in grams) altached to a coiled sprin...
 9.9.3.33: Distance to the Green A golfer hits an errant tee shot that lands i...
 9.9.1.33: Chicago Skyscrapers The angle of inclination from the base of the J...
 9.34: In 2534, find the area of each triangle. A = 10, C = 40, c = 3
 9.9.2.34: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.34: Area of a Segment Find the area of the segment of a circle whose ra...
 9.9.5.34: In 3338, an object of mass m (in grams) altached to a coiled sprin...
 9.9.3.34: Navigation An airplane flies due north from Ft. Myers to Sarasota, ...
 9.9.1.34: Estimating the Width of the Mississippi River A tourist at the top ...
 9.35: Finding the Grade of a Mountain Trail A straight trail with a unifo...
 9.9.2.35: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.35: Cost of a Triangular Lot The dimensions of a triangular lot are 100...
 9.9.5.35: In 3338, an object of mass m (in grams) altached to a coiled sprin...
 9.9.3.35: Avoiding a Tropical Storm A cruise ship maintains an average speed ...
 9.9.1.35: Finding the Pitch of a Roof A carpenter is preparing to put a roof ...
 9.36: Geometry The hypotenuse of a right triangle is 12 feet. If one leg ...
 9.9.2.36: In 2536, two sides and an angle are given. Determine whether the g...
 9.9.4.36: Amount of Material to Make a Tent A coneshaped tent is made from a...
 9.9.5.36: In 3338, an object of mass m (in grams) altached to a coiled sprin...
 9.9.3.36: Revising a Flight Plan In attempting to fly from Chicago to Louisvi...
 9.9.1.36: Shooting Free Throws in Basketball The eyes of a basketball player ...
 9.37: Finding the Height of a Helicopter Two observers simultaneously mea...
 9.9.2.37: Rescue at Sea Coast Guard Station Able is located 150 miles due sou...
 9.9.4.37: Dimensions of Home Plate The dimensions of home plate at any major ...
 9.9.5.37: In 3338, an object of mass m (in grams) altached to a coiled sprin...
 9.9.3.37: Major League Baseball Field A Major League baseball diamond is actu...
 9.9.1.37: Geometry Find the value of the angle e in degrees round ed to the n...
 9.38: D etermining Distances at Sea Rebecca, the navigator of a ship at s...
 9.9.2.38: Surveying Consult the figure to the right. To find the distance fro...
 9.9.4.38: Computing Areas Find the area of the shaded region enclosed in a se...
 9.9.5.38: In 3338, an object of mass m (in grams) altached to a coiled sprin...
 9.9.3.38: Little League Baseball Field According to Little League baseball of...
 9.9.1.38: Surveillance Satellites A surveillance satellite circles Earth at a...
 9.39: Constructing a Highway A highway whose primary directions are north...
 9.9.2.39: Finding the Length of a Ski Lift Consul t the figure. To find the l...
 9.9.4.39: Geometry Consult the figure, which shows a circle of radius r with ...
 9.9.5.39: In 3944, the distance d (in meters) of the bob of a pendulum of ma...
 9.9.3.39: Finding the Length of a Guy Wire The height of a radio tower is 500...
 9.9.1.39: The Gibb's Hill Lighthouse, Southampton, Bermuda In operation since...
 9.40: Correcting a Navigational Error A sailboat leaves St. Thomas bound ...
 9.9.2.40: Finding the Height of a Mountain Use the illustration in t o find t...
 9.9.4.40: Approximating the Area of a Lake To approximate the area of a lake,...
 9.9.5.40: In 3944, the distance d (in meters) of the bob of a pendulum of ma...
 9.9.3.40: Finding the Length of a Guy Wire See the figure below. A radio towe...
 9.41: Surveying Two homes are located on opposite sides of a small hill. ...
 9.9.2.41: Finding the Height of an Airplane An aircraft is spotted by two obs...
 9.9.4.41: The Flatiron Building Completed in 1902 in New York City, the Flati...
 9.9.5.41: In 3944, the distance d (in meters) of the bob of a pendulum of ma...
 9.9.3.41: Wrigley Field, Home of tbe Chicago Cubs The distance from home plat...
 9.42: Approximating the Area of a Lake To approximate the area of a lake,...
 9.9.2.42: Finding the Height of the Bridge over the Royal Gorge The highest b...
 9.9.4.42: Bermuda Triangle The Bermuda Triangle is roughly defined by Hamilto...
 9.9.5.42: In 3944, the distance d (in meters) of the bob of a pendulum of ma...
 9.9.3.42: Little League Baseball The distance from home plate to the fence in...
 9.43: Calculating the Cost of Land The irregular parcel of land shown in ...
 9.9.2.43: Landscaping Pat needs to determine the height of a tree before cutt...
 9.9.4.43: Geometry Refer to the figure. If 10AI = 1, show that: (a) Area AOAC...
 9.9.5.43: In 3944, the distance d (in meters) of the bob of a pendulum of ma...
 9.9.3.43: Building a Swing Set Clint is building a wooden swing set for his c...
 9.44: Area of a Segment Find the area of the segment of a circle whose ra...
 9.9.2.44: Construction A loading ramp 10 feet long that makes an angle of 18 ...
 9.9.4.44: Geometry Refer to the figure, in which a unit circle is drawn. The ...
 9.9.5.44: In 3944, the distance d (in meters) of the bob of a pendulum of ma...
 9.9.3.44: Rods and Pistons Rod OA rotates about the fixed point 0 so that poi...
 9.45: Finding the Bearing of a Ship The Majesty leaves the Port at Boston...
 9.9.2.45: Commercial Navigation Adam must fly home to St. Louis from a busine...
 9.9.4.45: The Cow Problem':' A cow is tethered to one corner of a square barn...
 9.9.5.45: Loudspeaker A loudspeaker diaphragm is oscillating in simple harmon...
 9.9.3.45: Geometry Show that the length d of a chord of a circle of radius r ...
 9.46: Drive Wheels of an Engine TIle drive wheel of an engine is 13 inche...
 9.9.2.46: Time Lost due to a Navigation Error In attempting to fly from city ...
 9.9.4.46: Another Cow the barn in is rectangular, 10 feet by 20 feet, what is...
 9.9.5.46: Colossus Added to Six Flags St. Louis in 1986, the Colossus is a gi...
 9.9.3.46: For any triangle, show that cos f = 2 "V 1 where s = 2 (a + b + c)....
 9.47: Rework if the belt is crossed, as shown in the figure.
 9.9.2.47: Finding the Lean of the Leaning Tower of Pisa The famous Leaning To...
 9.9.4.47: Perfect Triangles A perfect triangle is one having natural number s...
 9.9.5.47: Tuning Fork The end of a tuning fork moves in simple barmonic motio...
 9.9.3.47: For any triangle show that . C )r:"(  a:) (:  s b) Sln  = 2...
 9.48: In 48 and 49, an object attached to a coiled spring is pulled down ...
 9.9.2.48: Crankshafts on Cars On a certain automobile, the crankshaft is 3 in...
 9.9.4.48: If hI, h2' and h3 are the altitudes dropped from P, Q, and R, respe...
 9.9.5.48: Tuning Fork The end of a tuning fork moves in simple harmonic motio...
 9.9.3.48: Use the Law of Cosines to prove the identity cos A cos B cos C a2...
 9.49: In 48 and 49, an object attached to a coiled spring is pulled down ...
 9.9.2.49: Constructing a Highway U.S. 41, a highway whose primary directions ...
 9.9.4.49: Show that a formula for the altitude h from a vertex to the opposit...
 9.9.5.49: Charging a Capacitor See the illustration. If a charged capacitor i...
 9.9.3.49: What do you do first if you are asked to solve a triangle and are g...
 9.9.3.50: What do you do first if you are asked to solve a triangle and are g...
 9.50: In 5053, the distance d (in feet) that an object travels in time t...
 9.9.2.50: Calculating Distances at Sea The navigator of a ship at sea spots t...
 9.9.4.50: Inscribed Circle For 5053, Ihe lines (hal bisect each angle of a t...
 9.9.5.50: The Sawtooth Curve An oscilloscope often displays a . sawtooth curv...
 9.9.3.51: Make up an applied problem that requires using the Law of Cosines.
 9.51: In 5053, the distance d (in feet) that an object travels in time t...
 9.9.2.51: Designing an Awning An awning that covers a sliding glass door that...
 9.9.4.51: Inscribed Circle For 5053, Ihe lines (hal bisect each angle of a t...
 9.9.5.51: TouchTone Phones On a TouchTone phone, each button produces a uni...
 9.9.3.52: Write down your strategy for solving an oblique triangle.
 9.52: In 5053, the distance d (in feet) that an object travels in time t...
 9.9.2.52: Finding Distances A forest ranger is walking on a path inclined at ...
 9.9.4.52: Inscribed Circle For 5053, Ihe lines (hal bisect each angle of a t...
 9.9.5.52: Use a graphing utility to graph the sound emitted by the ,;, key on...
 9.53: In 5053, the distance d (in feet) that an object travels in time t...
 9.9.2.53: Great Pyramid of Cheops One of the original Seven Wonders of the Wo...
 9.9.4.53: Inscribed Circle For 5053, Ihe lines (hal bisect each angle of a t...
 9.9.5.53: CBL Experiment Pendulum motion is analyzed to esti,. mate simple ha...
 9.54: In 54 and 55, an object of mass m attached to a coiled spring with ...
 9.9.2.54: Determining the Height of an Aircraft Two sensors are spaced 700 fe...
 9.9.4.54: What do you do first if you are asked to find the area of a triangl...
 9.9.5.54: CBL Experiment The sound from a tuning fork is collected over time....
 9.55: In 54 and 55, an object of mass m attached to a coiled spring with ...
 9.9.2.55: Mercury The distance from the Sun to Earth is approximately 149,600...
 9.9.4.55: What do you do first if you are asked to find the area of a triangl...
 9.9.5.55: Use a . graphing utility to graph the function sm x f(x) = , x > ...
 9.56: In 56 and 57, the distance d (in meters) of the bob of a pendulum o...
 9.9.2.56: Venus The distance from the Sun to Earth is approximately 149,600,0...
 9.9.5.56: Use a graphing utility to graph y = x sin x, y = x2 sin x, and r. y...
 9.57: In 56 and 57, the distance d (in meters) of the bob of a pendulum o...
 9.9.2.57: The Original Ferris Wheel George Washington Gale Ferris, Jr. design...
 9.9.5.57: U h' t h I . 1 . :J7. se a grap mg utI Ity to grap y =  sm x, y = ...
 9.58: In 58 and 59, use the method of adding ycoordinates to graph each ...
 9.9.2.58: Mollweide's Formula For any triangle, MoUweide's Formula (named aft...
 9.9.5.58: How would you explain to a friend what simple harmonic motion is? H...
 9.59: In 58 and 59, use the method of adding ycoordinates to graph each ...
 9.9.2.59: Mollweide's Formula Another form of Mollweide's Formula is ab sin[...
 9.9.2.60: For any triangle, derive the formula a = b cos C + c cos B [Hint: U...
 9.9.2.61: Law of Tangents For any triangle, derive the Law of Tangents. a b ...
 9.9.2.62: Circumscribing a Triangle Show that sin A a sin B sin C b c 1 2,. w...
 9.9.2.63: Make up three problems involving oblique triangles. One should resu...
 9.9.2.64: What do you do first if you are asked to solve a triangle and are g...
 9.9.2.65: What do you do first if you are asked to solve a triangle and are g...
Solutions for Chapter 9: Applications of Trigonometric Functions
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9780132329033
Solutions for Chapter 9: Applications of Trigonometric Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Since 328 problems in chapter 9: Applications of Trigonometric Functions have been answered, more than 58511 students have viewed full stepbystep solutions from this chapter. Chapter 9: Applications of Trigonometric Functions includes 328 full stepbystep solutions.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).