Question

If `sectheta = a` and `sintheta < 0`, find the exact valaues of `sintheta`?

I think the answer is like `-sqrt(a^2-1)`

Thanks in advance!!!

Answer 1

See below

Explanation:

`sectheta=a` and `sin theta>0`

`sectheta=1/costheta=a`

Squaring both sides

`1/cos^2theta=a^2`

`1/a^2=cos^2theta=1-sin^2theta`

Then, transposing terms

`sin^2theta=1-1/a^2`

`sin theta=+-sqrt(1-1/a^2)=+-sqrt(a^2-1)/a`

However `sintheta <0`, then `sintheta=-sqrt(a^2-1)/a`