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 of arc (or angle) t is in Quadrant 3. Its tan is positive.
`tan t = y/x = (-4)/-3 = 4/3`
`cot t = 1/(tan) = 3/4`
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 16/9) = 9/25`
`cos t = - 3/5` (cos t negative because t is in Q. 3)
`sin t = cos t.tan t = (-3/5)(4/3) = - 4/5`
`sec t = 1/(cos) = - 4/3`
`csc t = 1/(sin) = - 5/4`