Find sin(2x), cos(2x), and tan(2x) from the given information. csc(x) = 8, tan(x) < 0

Question

I have found cos(2x)= 31/32

I thought I found the correct answer for the other two... tan(2x)= 3 square root 7 over 31 and sin(2x)= 3 square root 7 over 32

but it Is saying my answer is incorrect for those two. Is there a different way I should be writing it? or are they just completely incorrect?

Answer 1

Csc(x) = 8, then Sin(x) = 1/8 and Cos(x) = -√63 / 8 in the 2nd quadrant.

Angle x = Sin^-1(1/8) = 7.18° but it is in the 2nd quadrant so 180° - 7.18° = 172.82°

So Sin(2x) = -0.248 in 4th quadrant

Cos(2x) = 0.969 " " " "

Tan(2x) = -0.257 " " " "