Question

How to solve `4sintheta=3cosectheta` if `0<x<360`?

The answer is `theta=60, 120, 240 and 300` degrees, but I can only find the answer `theta=60, 120` degrees, for some reason.

Answer 1

Below

Explanation:

`4sintheta=3cosectheta`

`4sintheta=3/sintheta`

`4(sintheta)^2=3`

`(sintheta)^2=3/4`

`sintheta=+-sqrt(3/4)`

`sintheta=+-(sqrt3)/2`

`sintheta=(sqrt3)/2` or `sintheta=-(sqrt3)/2`

`theta=60,120,240,300`

A common mistake is that when you square root a number, you always have to make sure you have the `+-` in front because if you square a positive or negative number, both will end up having a positive answer

ie `(-2)^2=4` and `2^2=4`