Question

The point `(-4,1)` is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?

Answer 1

`sin t = 1/sqrt17`
`cos t = - 4/sqrt17`

Explanation:

Point (x = -4, y = 1) on the terminal side is in the Quadrant 2.
Call t the angle (arc):
`tan t = y/x = - 1/4`
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 1/16) = 16/17`
`cos t = +- 4/sqrt17`
Since t lies in Quadrant 2 --> cos t is negative.
`cos t = - 4/sqrt17`
`sin^2 t = 1 - cos^2 t = 1 - 16/17 = 1/17`
`sin t = +- 1/sqrt17`
Since t lies in Quadrant 2 --> sin t is positive
`sin t = 1/sqrt17`