If cos x = 8/17 and 270° < x < 360°, what is sin(2x)

Question

Please write the fraction in simplest form thank you so much for helping

Answer 1

If cos x = 8/17 and  270º < x < 360º, then

sin x = -√(1 -(8/17)²,

sin x = -√((289-64)/289),

sin x = -√225/289

sin x = -15/17.

 

We use sin 2x formula:

sin 2x = 2 (sin x)(cos x),

sin 2x = 2 (-15/17)(8/17)

sin 2x = - 240/289.