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Final Exam Review Questions Trigonometry NOTE: You will be able to use your calculator for the entire final exam. Chapter 1: 1) Find sin , cos , tan if is an angle in standard position having the point (–4, 3) on its terminal side. 2) Find tan and sec if sin 12 13 and cos 0 . 3) Use the Pythagorean identities to find sin , cos , tan if sec 5 with in quadrant IV. 4 4) Convert 70.12 to DMS form. 5) Find the angle of smallest possible positive measure coterminal with 210 Chapter 2: 6) Find the six trigonometric values for the given angle 150 7) Find the six trigonometric values for the given angle 420 8) Evaluate the expression and give the exact value. cos 2 45 2 sin 150 9) Find the decimal approximation of cos 425 32' 10) Find the decimal approximation of sec 95.29 11) A radio technician is at a spot that has an angle of elevation of 18.5 to the top of a 255-foot-tall transmitting antenna. How far is the radio technician from the base of the transmitting antenna? 12) Find the reference angle for 522.87 13) Use a calculator to find the decimal approximation for csc 132 44' Chapter 3: 14) Convert 225 to radians. 15) Convert 11 to degrees. 6 16) Give the exact value of tan 9 . 4 17) Give the exact value of cos 135 = 18) Give the exact value of sec 5 3 19) Use a calculator to find cot 5.2398 20) Find the arc length in the figure below. 21) Find the radius of a circle in which the central angle of 2 radians intercepts an arc of length 3 feet. Chapter 4: 22) What is the period of y 3 2 sin x? 4 23) Graph one period of each of the following. State the amplitude (A), period (P), vertical shift (V.S.), and phase shift (P.S.). Show all critical points as well as labeling the axes. a. y 3 3 cos x 1 b. y 2 3 cos x 2 2 3 c. y sin x 1 2 2 d. y csc x 4 1 e. y cot x 2 2 f. y 4 sec x 2 Chapter 5: 24) Use the sum and difference identities to find the exact value of : cos 5 12 5 4 6 12 5 4 with x in quadrant III and sin y with y in quadrant IV, find: 5 5 a. sin (x – y) 25) Given that cos x b. cos (x – y) 26) Verify the following identities a. 2 cot x sin x cos x 2 2 sin 2 x b. cos 2 x sec x 2 cos x sec x cos x cos3 x c. sin x cos x sin x d. (1 cos 2 x )(1 cos2 x ) 2 sin 2 x sin 4 x e. sin x cot x csc x 1 cos x 1 tan x f. tan x 4 1 tan x Chapter 6: 27) Give the exact radian value for each of the following. 1 a. cos1 2 b. sec 1 2 c. tan 1 3 3 3 d. sin 1 2 28) Give the exact degree value for each of the following. Round your answers to 2 decimal places. a. sec 1 (3) b. csc 1 (5.5) c. cot 1 (.78643) 29) Solve each equation for solutions 0, 2 . a. 2 cos4 x cos 2 x b. 41 sin x 1 sin x 3 c. cos 2 x cos x 0 Chapter 7: 30) Use the law of sines and/or law of cosines to solve the following triangles: a. A 37 B 48 c 18 b. C 28.3 a 5.71 b 4.21 c. a = 16 b = 17 c = 19 31) Two lighthouses are located on a north-south line. From lighthouse A, the bearing of a ship 2742 meters away is 11141 . From lighthouse B, the bearing of the ship is 3251 . Find the distance between the lighthouses.