Question

How do you find the remaining trigonometric functions of `theta` given `tantheta=a/b` where a and b are both positive?

Answer 1

Please see below.

Explanation:

As `tantheta=a/b`, `cottheta=1/(a/b)=1xxb/a=b/a`

`sectheta=+-sqrt(1+tan^2theta)=+-sqrt(1+a^2/b^2)=+-sqrt(a^2+b^2)/b`

`costheta=+-b/sqrt(a^2+b^2)`

`sintheta=tanthetaxxcostheta=+-a/bxxb/sqrt(a^2+b^2)=+-a/sqrt(a^2+b^2)`

and `csctheta=+-sqrt(a^2+b^2)/a`