Question

How do you sketch the angle whose terminal side in standard position passes through (-8,15) and how do you find sin and cos?

Answer 1

`sin t = 15/17`
`cos t = - 8/17`

Explanation:

The point (x = -8, y = 15), on the angle terminal side, lies in Quadrant 2. Call t the angle.
`tan t = y/x = - 15/8`
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 225/64) = 64/289`
`cos t = +- 8/17`
Because t lies in Quadrant2, --> cos t is negative:
`cos t = - 8/17`
`sin^2 t = 1 - cos^2 t = 1 - 64/189 = 125/189`
`sin t = +- 15/17`
Because t lies in Quadrant 2, --> sin t is positive.
`sin t = 15/17`