20 MCQs on Plane Trigonometry - Exam II | MATH 026, Exams of Trigonometry

Download 20 MCQs on Plane Trigonometry - Exam II | MATH 026 and more Exams Trigonometry in PDF only on Docsity! MATH 026 EXAM II SAMPLE B 1. Simplify cos x sin ( π 2 − x ) + sin(−x). a) cos x sin x + sin x b) cos2 x + sin x c) cos2 x− sin x d) cos x sin x− sin x e) cos2 x + cos x 2. Simplify cot2 ( 5π 7 ) − csc2 ( 5π 7 ) . a) 2 cos2 ( 5π 7 ) b) 2 cot2 ( 5π 7 ) c) 0 d) -1 e) 1 3. Find an equivalent expression for sin t + cos t cot t. a) sec t b) csc t c) tan t d) cot t e) 1 4. Simplify sin2 x− sin2 y + cos2 x− cos2 y. a) 2 b) 1 c) 0 d) -1 e) -2 5. Factor the expression tan2 x− 3 tan x + 2. a) (tan x− 1)(tan x− 2) b) (tan x + 1)(tan x + 2) c) tan x(tan x + 2) d) tan ( (x− 1)(x− 2)) e) (x− 1)(x + 2) 6. Write an equivalent factored expression for 1 + sinx− cos2 x. a) (1 + sin x) cos2 x b) sin x(1 + sin x) c) (1 + cos x)(1− cos x) d) (sin x + 2)(sin x + 1) e) (1 + cos x) cos(x) 7. Find an equivalent expression for 1− sin2 x sin2 x . a) sin2 x b) cos2 x c) tan2 x d) cot2 x e) sec2 x 8. Simplify cos2(44◦) + cos2(46◦). a) 1 b) -1 c) 2 cos2(44◦) d) 2 cos2(46◦) e) 2 sin2(44◦) 9. How many solutions are there to √ 3 sec x− 2 = 0 for 0 ≤ x < 2π? a) 0 b) 1 c) 2 d) 3 e) 4 10. Which of the following is the complete list of solutions to 2 cos2 x− cos x = 0 for 0 ≤ x<2π. a) 0, π, π 6 , 11π 6 b) π 2 , 3π 2 c) π 6 , 11π 6 d) 0, π e) π 2 , 3π 2 , π 3 , 5π 3 1 MATH 026 EXAM II SAMPLE B 11. Find the general form(s) of the solutions to 2 sin(x)− √ 2 = 0. a) π 4 , 3π 4 b) π 4 + 2nπ c) 3π 4 + 2nπ d) π 4 + nπ, 3π 4 + nπ e) π 4 + 2nπ, 3π 4 + 2nπ 12. Which of the following is a solution to sin5 x− 1 = 0? a) 0 b) π 2 c) π 6 d) π 4 e) π 3 13. Find the exact value of cos 105◦. a) ( √ 2− √ 6)/4 b) ( √ 2 + √ 6)/4 c) (− √ 2− √ 6)/4 d) ( √ 6− √ 2)/4 e) √ 3/2 14. Which of the following is equal to 1 2 sin 11◦ + √ 3 2 cos 11◦? a) sin 11◦ b) sin 19◦ c) sin 41◦ d) sin 49◦ e) sin 71◦ 15. Simplify sin ( π 2 − x ) + sin ( π − x ) . a) 0 b) cos(x)− sin(x) c) cos(x) + sin(x) d) 2 cos(x) e) 2 sin(x) 16. Find an equivalent expression for tan 2x + tan x 1− tan 2x tan x . a) tan x b) tan 2x c) tan 3x d) tan(−x) e) 0 17. Find the exact value of sin(15◦). a) 1 2 b) 1 4 c) √ 3 4 d) √ 6 + √ 2 4 e) √ 6−√2 4 18. If sin x = 1 3 , find cos 2x. a) 2 3 b) √ 5 3 c) 2 9 d) 7 9 e) 4 9 19. How many solutions are there to 2 sin x = sin 2x for 0 ≤ x<2π. a) 0 b) 1 c) 2 d) 3 e) 4 2