Determine the exact value of the following trigonometric fun

Determine the exact value of the following trigonometric functions given that cos(theta) = - 60/65 and the terminal ray of an angle with a measure of theta radians lies in Quadrant III. sin(theta) = The terminal ray of an angle with a measure of 2 theta radians lies in Quadrant sin(2 theta) = cos(2 theta)

Solution

cos(theta) = -60/65 ; theta is in Q III

a) sintheta= sqrt(1 - cos^2theta) = -sqrt( 1- (60/65)^2)

= - 25/65

b) sin2theta = 2sintheta*costheta = 2*(-25/65)*(-60/65) = 3000/4225

c) cos2theta = 2cos^2theta -1 = 2(-60/65)^2 -1 = 2975/4225