Trigonometry Final Exam Review

Transcription

1 Name Period Trigonometry Final Exam Review CHAPTER 2 RIGHT TRIANGLES 8 1. Given sin θ = and θ terminates in quadrant III, find the following: 17 a) cos θ b) tan θ c) sec θ d) csc θ 2. Use a calculator to evaluate each of the following. Round nearest ten-thousandth. a) sin 25 b) tan 170 c) csc 146 d) cot Rewrite each of the following using the cofunction identities. a) sin 18 b) cos 34 c) tan 10 d) sec A flagpole is casting a shadow of 30 meters. The angle of elevation created by the end of the shadow and the top of the flagpole is 36. How tall is the flagpole? 5. A 20 foot ladder leans against a wall. The top of the ladder reaches a point 18 feet high. Find the angle formed by the ladder and the ground. 6. A ship sails on a bearing of N 67 E for 183 miles. How far north and how far east is the ship from its starting point?

2 CHAPTER 3 RADIAN MEASURE 7. Convert from degrees to radians or from radians to degrees. a) 80 b) 2 π c) 230 d) 5 4π 9 8. A Ferris wheel has a radius of 50 ft. Find the distance traveled by a rider if he has rotated 150 from his starting point. 9. A bicycle wheel with a diameter of 2.6 ft has an angular velocity of 46π radians per minute. Find its linear velocity. 10. Convert 72 rpm (revolutions per minute) to an angular velocity in radians per minute. 11. A CD rotates at 83 rpm. Find its linear velocity at a point 2 inches from the center of the CD. 12. The diameter of a pizza is 16 inches. If a slice of pizza is cut with a central angle of 62, find the area of the slice of pizza. (Assume the pizza is circular.)

3 THE UNIT CIRCLE 13. State a positive and a negative coterminal angle for each of the following: a) 687 b) 22 π Determine the quadrant of each of the following: a) 3 π b) Give the coordinates of each of the following angles on the unit circle: a) 240 b) 330 c) 5 π 6 d) 16π Define each of the following in terms of x and y, a) tanθ b) secθ c) cotθ d) cscθ 17. Determine the sign (+ or ) of each of the following: 9π a) tan b) cos 378 c) 8 π 2 csc 5 d) cot Determine the exact value of each of the following: 17π a) sin b) cos( 930 ) c) sec 240 d) 3 11π tan Solve for θ in the given interval. a) sin θ = ½ where 0 < θ < 2π b) cos θ = 3 2 where 0 < θ < 360 c) tan θ = 1 where 0 < θ < 2π d) csc θ = 2 where 0 < θ < 360

4 CHAPTER 4 GRAPHING 20. Determine each of the following: a) the amplitude of y = 5 cos (2x) + 9 b) the period of y = 4 sin (4x) 7 c) the vertical shift of y = 4 sin (4x) 7 d) name one asymptote in y = 2 cot (3x) 2 Graph one period of each function. Also find the period, amplitude, domain, and range. Make sure to label all critical values. 21) y = 2 sin (3x) ) y = 3cos(2(x π )) ) y = -3csc x - 2

5 24) y = 2 sec (3x 3π) +1 25) y = 2cot(x π )) ) y = 2 tan( π (x 2)) +1 3

6 CHAPTER 5 - IDENTITIES 27) True or False: a) sin 2 θ cos 2 θ = 1 b) 1 + cot 2 θ = csc 2 θ c) 2 2cos 2 x = 2sin 2 x d) tan θ 1 = sec θ 28) Define each of the following in terms of sinθ and cosθ. a) tanθ b) secθ c) cotθ d) cscθ 29) Prove the following identity: sin 2 t sec 2 t + sin 2 t csc 2 t = sec 2 t 30) Given sin A = 4 5 with A terminating in QI and cos B = with B terminating in QIV, find a) cos (A + B) b) sin (A + B) c) Quadrant of (A+B)

7 3 31) Given sin A = with A terminating in QIV, find 5 a) sin 2A b) sec 2A c) tan 2A d) The angle 2A is in Quadrant 32) Given cos A = with A terminating in QIII, find a) cos A 2 b) csc A 2 c) tan A 2 d) The angle A 2 is in Quadrant

8 CHAPTER 6 - EQUATIONS 33) Factor: 8 sin 2 x 32 cos 2 x 34) Factor: 2 cot 2 x 3 cot x 20 35) Find the reference angle for each of the following: a) 314 b) 147 Calculate the value(s) of θ, where 0 < θ < 360. Also find the reference angle and quadrants. Round to the nearest tenth. 36) sin θ = ) tan θ = ref angle = quadrants: ref angle = quadrants: θ = θ = 38) sec θ = ) cot θ = ref angle = quadrants: ref angle = quadrants: θ = θ =

9 Solve the following equations in radians on the interval [0, 2π). 40) 3sec θ = 6 41) tan 2 θ = 3 42) 2sin θ = 4 43) 9csc θ 7 = 2 Solve the following equations on the interval [0, 360 ). Round to the nearest tenth when necessary. 44) 2sin 2 θ 5sinθ 3 = 0 45) 4cos 2 x +7cos x 2 = 0 46) (3sin x 1) (2tan x + 3) = 0 47) sinθ + 2cos 2 θ 1 = 0 48) sin (2x) = 2sin x 49) 3cscx sin x = 2

10 CHAPTER 7 OBLIQUE TRIANGLES 50) Find the missing pieces of information of triangle Δ PRQ if R = 90, P = 39, and p = 11.7 cm. 51) In ΔABC, A = 48, b = 13.2 cm and c = 16.8 cm, find 52) In ΔABC, A = 67, B = 85, and c = 14 inches, find

11 53) In ΔABC, A = 12, a = 24 m, and c = 29 m, find Find the area of ΔABC 54) a = 8 ft, b = 10 ft, and c = 12 ft 55) A = 38, b = 6 mi, and c = 4 mi.