Question

How do you find the sin(Θ) of an angle in standard position if the terminal side passes through the point (4, -8)?

Answer 1

`- (2sqrt5)/5`

Explanation:

Call t the angle that is in Quadrant 4.
`tan t = -8/4 = - 2`
Use trig identity:
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 4) = 1/5`
`cos t = +- 1/sqrt5`
Because t is in Quadrant 4, then, cos t is positive.
`sin t = cos t.tan t = (1/sqrt5)(-2) = -2/sqrt5 = - (2sqrt5)/5`