MAT 141 EXAM 2 1) The point Plky) is on the unit circle in quadrant.ind y 2 If c

Question

MAT 141 EXAM 2 1) The point Plky) is on the unit circle in quadrant.ind y 2 If cos t iand if the terminal point t is in quadrant 3, find the value of tan t cott +csct. 3) For the function y 2 sinx-, find the a) amplitude b) period c) phase shift d) sketch the graph of one complete period 4) Prove that tan x sin x + cos x sec x 5) Simplify each of the following trigonometric expressions b) sin x cos'x -sin x a) sin t+ cot t cos t 6) Show that cos (9-3 )--sin ? 7) Use the half-angle formula to find the exact value of a) sin 105° b) cos NB: half-angle must be written in radians

Explanation / Answer

1) x = sqrt 11/ 6

since its a unit circle

r = 1

so, y = sqrt [ 1^2 - (sqrt 11/6 )^2 ]

y = sqrt [ 25/ 36 ]

y = 5/6

2) cos t = - 8/17

base = 8 , hypotenuse = 17

perpendicular = sqrt [ 17^2 - 8^2 ]

perpendicular = 15

tan t = 15/8

cot t = 8/15

csc t = - 17/15

tan t cot t + csc t

= 15/8 * 8/15 - 17/15

= 1 - 17/15

= - 2/15

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