If cos ⁡θ= −8/17, and 180°θ<270°, what is sin θ?

Question

If cos ⁡θ=−8/17, and 180°θ<270°, what is sin θ?

Answer 1

sine is -15/17

cosine is adjacent side over hypotenuse

sine is opposite side over hypotenuse

180 to 270 is the 3rd quadrant where both sine and cosine are negative

8/17 means the opposite side is the square root of (17 squared minus 8 squared)

or sqr [17^2-8^2]= sqr(289-64) = sqr225 = 15

sine of theta is -15/17

This is a right triangle with sides 8, 15, and 17 in the 3rd quadrant where

only the hypotenuse is positive