Asked by Anonymous

What is cos 2theta for sin theta = -2/13 in 180 degs < theta < 270 degs?

Answers

Answered by Reiny
sinØ = -2/13 and we are told Ø is in III

so y = -2, r = 13
x^2 + y^2 = r^2
x^2 + 4 = 169
x= ±√165 , but in III x = -√165

cosØ = -√165/13

cos 2Ø = cos^2 Ø - sin^2 Ø
= 165/169 - 4/169

= 161/169
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