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Practice Test Ch 5 pg1 Math 240 Instructor: Butler Practice Quiz Chapter 5 Do not use a calculator for this test. 1. Fill in the blank a) tan x = ______________ (Negative-Angle Identity) b) 1 sin 2 x = ______________ (Pythagorean Identity) c) sin 2 A = _______________ (Double Angle Identity) d) cos 2 A = cos 2 A sin 2 A e) cos f) sin 90 = cos ____________________ g) tan 2 1 = sec 2 ____________________ h) sec = _________________ (Reciprocal Identity) i) cos A B = ____________________ (Cosine Difference Identity) j) cot90 = __________________ (Cofunction Identity) ____________________ A = ________________ (Half-Angle Identity) 2 2. Use the fundamental identities to find the remaining five trigonometric functions of θ. 1 cos a) in Quadrant I 5 3. Verify the identity. Show all your work, and all the steps. a) tan cot sec csc b) csc cos 2 sin csc c) sin 2 x 2 sin x sec x Practice Test Ch 5 pg2 4. Use the sum and difference identities to find the exact values. 5 a) cos15 b) sin c) sin 105 12 d) tan 80 tan 55 1 tan 80 tan 55 2 1 and sin t , s is in quadrant II and t is in quadrant IV, 3 3 a) find coss t b) find tan s t c) quadrant of s t 5. Given sin s 6. Use a double angle or half angle identity to write each expression as a single trigonometric function or a single number. 2 tan 15 1 1 cos 76 a) b) c) 1 2 sin 2 22 2 2 1 tan 15 2 7. Find the exact value of cos cos x = 2 x 5 given sin x and tan x > 0 2 8 1 cos x 2 ANSWERS 1.a) tan x 1.b) cos 2 x 1.f) Cofunction Id. 1.c) 2 sin Acos A 1.g) Pythagorean Id. 1.d) Double Angle Id. 1.h) 1 cos 7. 2. sin 8 39 4 1 cos A 2 1.i) cos A cos B sin A sin B 2 6 tan 2 6 sec 5 csc 5 6 2 6 2 6 2 4.a) 4.b) 4.c) 4.d) 1 5.a) 4 4 4 3 8 5 5 2 5.b) 5.c) Quadrant II 6.a) 6.b) cos 38 3 20 2 10 1.j) tan 1.e) 5 6 12 cot 2 10 2 9 2 6.c) 2 6 12