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MATH 1112A Test 2 Study Guide Part 1: Calculating Trigonometric Function Values using Identities a) Sum & Difference Identities b) Double/Half Angle Identities c) Inverse Trig Functions d) Composition of Functions Examples: Use identities and inverse trigonometric functions to calculate the exact values (NO decimals!) of each of the function values below. 4 sin(arcsin( )) 5 cos( ) 12 sin(2 cos 1 ( 20 )) 29 tan(cos 1 ( 1 3 cos(arccos( ) arcsin( )) 2 2 Part 2: Simplify Trig Expressions Examples: Simplify each of the following trigonometric expressions. Show all of your work. (1 sin x)(sec x tan x) sec x cos x tan x Part 3: Prove Trig Identities: Examples: Show all work and use correct logical structure. sin( x y ) sin( x y ) 2 cos x sin y sin(u v) cos u cos v 1 sin 2 1 1 sec csc sin 2 2 tan u tan v Part 4: Solve Trig Equations: Examples: a) Find the solutions on the interval [0,2π) tan 2 x tan x b) Find all solutions 2cos x 1 0 5sin 3 3 8 )) 17 Part 5: Miscellaneous 1. If A and B are positive acute angles, sin A of sin( A B ) ? 16 a) 65 2. b) 33 65 c) 5 4 , and cos B , what is the value 13 5 56 65 d) 63 65 12 3 , cos y , and x and y are acute angles, what is the value of 13 5 cos( x y ) ? 33 14 21 63 a) b) c) d) 65 65 65 65 If sin x 5 , what is the value of sin 2 ? 13 60 120 c) d) 169 169 3. If is an acute angle such that sin a) 10 26 b) 12 13 4. The expression (1 cos x)(1 cos x) is equivalent to a) 1 b) sin 2 x 5. The expression a) sin 6. The expression a) sin 7. The expression a) cos 2 sin c) sec2 x d ) csc2 x 2 cos is equivalent to sin 2 b) sec c) csc d ) cot sec is equivalent to csc b) cos c) tan d ) cot tan is equivalent to sec sin b) c) sin cos 2 d ) cos 8. The expression cos 40 cos10 sin 40 sin10 is equivalent to a) cos30 b) cos50 c) sin30 d ) sin50 9. What value of x in the interval 0 x 180 satisfies the equation 3 tan x 1 0? a) 30 b) 30 c ) 60 d ) 150 Resource: New York Math B Regents