Use the figure below to find the exact values of the double

Use the figure below to find the exact values of the double angles. Find sin(2 beta), cos(2 beta) tan(2 beta). sin(2 alpha), cos(2 alpha), and tan(2 alpha). sin(2 beta) = cos(2 beta) = tan(2 beta) = sin(2 alpha) = cos(2 alpha) = tan(2 alpha) =

Solution

Base = B = 15

Hyp = H = 17

Perp = P = 8

Cos = sin = 15/17

sin = cos = 8/17

tan = 8/15

tan = 15/8

Now sin 2 = 2*sin*cos = 2*8/17*15/17 = 0.8304

cos2 = 2*cos^2 - 1 = 2*(15/17)^2 - 1 = 0.557

tan 2 = 2*tan/(1 - tan^2 ) = 2*(8/15)/(1 - (8/15)^2) = 1.4907

sin 2 = 2*sin*cos = 2*8/17*15/17 = 0.8304

cos2 = 2*cos^2 - 1 = 2*(8/17)^2 - 1 = -0.557

tan 2 = 2*tan/(1 - tan^2 ) = 2*(15/8)/(1 - (15/8)^2) = -1.4907