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MATH 1112 FINAL EXAM REVIEW I. State the equation of the unit circle. II. If cot x III. Simplify each expression. IV. V. VI. 12 , find sin x for x in Quadrant II. 5 1. 3 sin 2 2. cos 3. sin150 4. sin 660 5. 3 cos 4 6. cos0 7. tan315 8. cot 9. 5 sec 6 10. csc0 Sketch the graph of each function on [0, 2 ) . 1. y sin x 2. y cos x 3. y tan x 4. y cot x 5. y sec x 6. y csc x Simplify each expression. 1. cos( ) 2. sin( ) 3. tan( ) 4. sec( ) 2. 3 cos 1 2 Evaluate each expression. 1. 2 arc sin 2 3. VII. VIII. IX. X. 3 sec cot 1 4 4. tan 1 1 Sketch at least one cycle of the graph of each function. 1. y 3sin 2 x 2. y 2cos x 3 3. y tan x 3 4. y cot 2 x 5. y 2sec3x Use the sum or difference identities to evaluate each expression. 1. cos 75 3. tan195 Let α be in Quadrant I, β in Quadrant III, cos 1. cos ? 2. sin ? 3. tan ? Change each sum or difference to a product. 1. sin 68 sin32 2. sin5x sin3x 3. cos12x cos5x 4. cos 20 cos 40 2. sin 285 7 5 , and tan . 25 12 XI. XII. XIII. Let θ be in Quadrant II with sec 1. sin 2 ? 3. tan 2 ? 13 . 5 2. cos 2 ? Evaluate each of the following expressions using the half-angle identities. 1. sin112.5 3. tan 67.5 2. cos157.5 If the terminal side of θ passes through the point (-3,2), find sin 2 . XIV. Solve each equation for 0 x 2 . 1. cos 2x 1 sin x 2. sin x cos x 3. 2 cos 2 x sin x 1 0 4. 3cot 2 2 x 1 0 1 2 XV. Solve ABC for the missing part. 1. A 90, a 29, b 21, B ? 2. a 5, b 8, c 10, C ? 3. A 40, b 6, B 20, c ? XVI. Give the radian measure of an angle that subtends an arc of length 24 in a circle of radius 8 . XVII. Convert 5 to degrees. 12 XVIII. Convert 260 to radians. XIX. Prove the following identities. 1. sin sec tan 2. sec2 tan 2 sec2 sec 4 3. csc sec cot tan sin cos 4. sin x cos x 2 1 sin 2 x XX. Simplify each expression. 1. sec4 x tan 4 x sec2 x tan 2 x 2. cos sin sin cos 3. tan 1 cos 2 XXI. Change the product to a sum. 1. 6sin15 sin 45 2. 4sin3x cos 2x 3 4 XXII. Let the point , be a point on the terminal side of an angle θ in standard 5 5 position. Find the sine and cosine of θ. XXIII. If tan 0 and cos 0 , in what quadrant is θ? XXIV. Give the reference angle for the indicated angle. 1. 211 3. 2.3 2. 5 9 2. 278 XXV. Find the quadrant in which the indicated angle lies. 1. 343 12 3. 5.43 4. 213 5 XXVI. Name one positive and one negative angle that is coterminal with the given angle. 1. 43 2. 13 12 ANSWERS: I. x2 y 2 1 II. 5 13 III. 1. 1 2. -1 3. 1 2 4. 5. 6. 1 7. -1 8. Undefined 9. 10. Undefined IV. 1. 2. 2 2 2 3 3 3 2 3. 4. 5. 6. V. VI. VII. 1. cos 2. sin 3. tan 4. sec 1. 2. 5 6 3. 4. 1. 4 5 3 2. 4 3. 4. 5. VIII. 3. IX. X. XI. XII. 6 2 4 1. 1. 3 3 32 3 3 204 325 2. 6 2 4 2. 323 325 323 36 3. 1. 2sin50 cos18 2. 2cos 4x sin x 3. 2 cos 17 x 7x cos 2 2 4. sin10 1. 2. 3. 120 119 2. 1. 120 169 2 2 2 119 169 2 2 2 2 2 2 2 3. XIII. 12 13 XIV. 1. 2. 3. 4. XV. 1. 3. 0, 6 , , 5 6 5 4 , 4 7 11 2 , 6 , 6 2 5 7 4 5 11 , , , , , , , 6 3 3 6 6 3 3 6 46.4 2. 97.9 2. csc sec 15.2 XVI. 3 XVII. 75 XVIII. 13 9 XX. 1. 1 3. csc sec XXI. 1. 3 3 3 2 2 2. 2sin5x 2sin x 4 3 XXII. sin , cos 5 5 XXIII. IV XXIV. 1. 3. XXV. 1. 3. 2. 4 9 II 2. I IV 4. III 31 .84 XXVI. *Answers may vary. I have given a couple of responses only. 1. 317, 403 2. 37 11 , 12 12