Find the exact values of sin 2 cos 2 and tan 2 for the given

Find the exact values of sin 2, cos 2, and tan 2 for the given value of .cot = 3/4

; 180° < < 270°

Find the exact values of sin(/2), cos(/2), and tan(/2) for the given condition.

3 tan = 3; 180° < < 90°

cot theta = 3/4

cot theta = base / perpendicular

base = 3 , perpendicular = 4

hypotenuse = sqrt ( 3^2 + 4^2) = 5
quadrant 3

sin theta = perpendicular / hyp = - 4/5

cos theta = base / hyp = - 3/5

sin 2 theta = 2 sin theta cos theta 2 ( -4/5) ( -3/5) = 24 / 25

cos 2 theta = cos^2 theta - sin^2 theta = ( -3/5)^2 - ( -4/5)^2 = 9/25 - 16/25 = -7/25

tan 2 theta = 2 tan theta / 1 - tan^2 theta = 2 (4/3) / 1 - (4/3)^2 = 8/3 / 1 - 16/9

tan 2 theta = -24/7