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MATH 30-1 TRIG 2 YEAR END REVIEW NUMERIC RESPONSE SECTION: x 2sin 3 x in radian mode, the largest x2 intercept, correct to the nearest tenth is _________. 1. Using your graphing calculator to graph y 2. Given that x is an acute angle, the value of x , correct to the nearest degree, such that sin x cot x 0.4 is _______. 3. The number of solutions to the equation cos 3 1 has over the interval 0 2 2 is ______. 4. Given that tan 3 is a fourth quadrant angle, determine the exact value of sin 2 cos 2 . 5. Each of the trigonometric ratios listed below results in a value of zero, or it will be undefined. tan 2 3 cot 2 sin csc 2 Use the following code to indicate that the value of the ratio is zero, or that the ratio is undefined. 1 = the ratio is zero 2 = the ratio is undefined RATIO: ________ ________ ________ ________ tan 2 3 cot 2 sin csc 2 6. Each trigonometric expression below can be simplified to a single numerical value. 1. cot 2 x csc2 x 2. sec2 x tan 2 x 3. sin x 4. 1 1 cos 2 x sin 2 x 7 7 tan x sec x When the numerical values of the simplified expressions are arranged in ascending order, the expression numbers are ____,____,____, and ____. WRITTEN RESPONSE: 2 tan x sin(2 x) n , where x ,n I . 2 2 2 1 tan x cos x sin x 4 2 1. Prove algebraically that 2. What is the exact value of tan 75 3. Find the general solution to the equation sin(2 ) cos 0 . Express the solution in degrees. MULIPLE CHOICE SECTION. 1. 2. Which of the following is true when if x positive and y negative, A. tan x , terminates in quadrant II y B. tan y , terminates in quadrant II x C. tan x , terminates in quadrant IV y D. tan y , terminates in quadrant IV x The solution to 2cos x 3 0 , for 0 x 2 is A. x B. x C. x D. x 3 3 6 6 ,x 2 3 ,x 5 3 ,x 5 6 x 11 6 3. If sin 4 , find two possible values of cos . 13 A. cos 153 13 B. cos 153 13 C. cos 153 13 D. none of the above 4. If the left side of an identity is sin x csc x , then the right side of the identity could be A. 0 B. 1 C. tan x D. sin 2 x 5. Angles x and y terminate in the same quadrant. If cos x sin( x y ) is A. 56 65 B. 59 60 C. 56 65 D. 59 60 3 13 and csc y , then 5 12 6. When the identity tan 2 A 2 tan A is verified for A , the left and right sides of 2 1 tan A 6 the identity are A. 0 B. 3 7. C. 3 D. 1 3 sin 3 x For the identity tan x to be valid, which of the following restrictions cos x cos3 x must be stated? A. cos x 0 B. cos x 0,1 C. cos x 1,1 D. cos x 0, 1,1 8. The exact value of cos A. cos B. cos C. cos D. cos 3 3 3 3 cos cos sin sin 4 4 4 4 12 can be determined by using sin sin cos cos 3 3 4 4 sin sin sin sin 4 4 3 3 9. If cot 3 and sin 0 , then the value of (sin cos )2 is: 4 A. 49 25 B. 6 25 C. 7 5 D. 10. 7 5 If the point 4, 2 lies on the terminal arm of an angle in standard position, determine the exact value of csc . A. - 5 B. 11. 5 2 C. 5 2 D. 5 The value of cos75 cos15 sin 75 sin15 is A. 1 B. 1 2 C. D. 0 3 2 12. In the interval 0 x 2 , the solutions of the equation sin 2 x sin x are A. 0, B. 13. , , 2 2 2 3 2 , , , 2 3 2 The complete set of solutions for 6sin 2 3 0 , 0 2 , is A. B. C. D. 14. 2 3 C. 0, D. 5 3 , 3 5 6 , 6 5 5 , , , 6 3 6 3 5 13 17 , , , 12 12 12 12 If 5sin x 2 6 cos 2 x where 0 x 2 , then one of the factors used to solve for x is A. 3sin x 4 B. 2sin x 1 C. 6sin x 1 D. sin x 1 15. Simplify sin( ) cos 2 A. 1 B. 1 C. tan D. tan 16. The expression sin x cos 2 x csc x is equivalent to A. sin 2 x B. tan 2 x C. csc x D. sec x