Question

Given `cottheta=-12/5` and `270<theta<360`, how do you find `csc (theta/2)`?

Answer 1

`rarrcsc(theta/2)=sqrt26`

Explanation:

Here, `270^(@)` `<` `theta` `<` `360^@`

`rarr135^(@)` `<` `theta/2` `<` `180^@` It means `theta/2` is in second quadrant where `sin and csc` are positive.

`rarrcottheta=-12/5`

`rarrtantheta=-5/12`

`rarrcostheta=1/sectheta=1/sqrt(1+tan^2theta)=1/sqrt(1+(-5/12)^2)=12/13`

`rarrcsc(theta/2)=1/sin(theta/2)=1/sqrt((1-costheta)/2)=1/sqrt((1-12/13)/2)=1/sqrt(1/(26))=sqrt26`