Question

How do you find all six trigonometric function of `theta` if the point `(-3,sqrt7)` is on the terminal side of `theta`?

Answer 1

`tan t = - sqrt7/3`, and t is in Quadrant 2.
Use trig identity:
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 7/9) = 9/16`
`cos t = +- 3/4`
Since t is in Quadrant 2, then, cos t is negative.
`cos t = - 3/4`
`sin t = tan t.cos t = (-sqrt7/3)(- 3/4) = sqrt7/4`
`cot t = 1/(tan) = - 3/sqrt7`
`sec t = 1/(cos) = - 4/3`
`csc t = 1/(sin) = 4/sqrt7 = (4sqrt7)/7`