Question

How do you find the remaining trigonometric functions of `theta` given `csctheta=13/5` and `costheta<0`?

Answer 1

`sintheta=5/13`, `costheta=-12/13`, `tantheta=-5/12`, `cottheta=-12/5`,
`sectheta=-13/12`;and `csctheta=13/5`

Explanation:

As `csctheta=13/5`, it is positive and as `costheta` is negative, `theta` lies in Quadrant II.

Now `sintheta=1/csctheta=1/(13/5)=5/13`

`costheta=-sqrt(1-(5/13)^2)=-sqrt(1-25/169)=-sqrt(144/169)=-12/13`

`tantheta=sintheta/costheta=(5/13)/(-12/13)=-5/13×13/12=-5/12`

`cottheta=1/tantheta=1/(-5/12)=-12/5`

`sectheta=1/costheta=1/(-12/13)=-13/12`