Question

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

Answer 1

`tan t = n/m`
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + n^2/(m^2)) = m^2/(m^2 + n^2)`
`cos t = +- m/(sqrt(m^2 + n^2))`
`sin^2 t = 1/(1 + cot^2 t) = 1/(1 + m/n) = n^2/(m^2 + n^2)`
`sin t = +- n/(sqrt(m^2 + n^2)`
`tan t = n/m`
`cot t = m/n`
`sec t = +- (sqrt(m^2 + n^2))/m`
`csc t = +- (sqrt(m^2 + n^2))/n`