Question

How do you find the exact value of `sintheta=csctheta` in the interval `0<=theta<360`?

Answer 1

`theta=90^0 and 270^0`

Explanation:

`sintheta=csctheta`
`sintheta=1/sintheta`

`sintheta^2=1`
`sintheta^2-1=0`

`(sintheta+1)(sintheta-1)=0`

`sintheta=-1`, `theta=sin^-1(-1)`
`theta=270^0`

`sintheta=1`, `theta=sin^-1(1)`
`theta=90^0`