Solve for Sin, Cos, and Tan

Question

If sin= -15/17 and x is in quadrant III, find the exact values of the expressions without solving for x.

a). sin(x/2)

b). cos(x/2)

c). tan(x/2)

Answer 1

sin x = -15/17

sin x ^2 + cos x^2 = 1

(-15/17)^2 + cos x^2 = 1

cos x^2 = 64/289

cos x = -8/17 (because in QIII)

sin(x/2) = +/- sqrt((1 - cosx)/2)

cos(x/2) = +- sqrt((1+ cosx)/2

tan(x/2) = sinx /(1 + cos x)