Question

How do you find all six trigonometric function of `theta` if the point (3,4) is on the terminal side of `theta`?

Answer 1

The terminal side, containing point (3, 4) is located in Quadrant 1.
Call t the angle:
`tan t = y/x = 4/3`
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 16/9) = 9/25`
`cos t = 3/5` (t in Quadrant 1 --> cos t is positive)
`sin^2 t = 1 - cos^2 t = 1 - 9/25 = 16/25`
`sin t = 4/5` (t in Quadrant 1 --> sin t is positive)
`tan t = 4/3`
`cot t = 1/(tan t) = 3/4`
`sec t = 1/(cos t) = 5/3`
`csc t = 1/(sin t) = 5/4`