basic identities

Question

if cosΘ=8/17, what is sinΘ?

Answer 1

The given trigonometric function determines the ratio of 2 sides of the triangle. So just draw a triangle with the given condition, use the Pythagorean Theorem to determine the 3rd side of the triangle, and then find the desired trig function.

For example, if tan(x) = √3, then the side opposite x could be √3 and the side adjacent to x would be 1. Then the hypotenuse would be 2, and sin(x) would be (√3)/2