Question

Suppose that cos(θ) =−3/5. Determine all possible values of tan(θ). ?

Answer 1

`tantheta=4/3, -4/3`

Explanation:

Recall the identity

`1+tan^2theta=sec^2theta`. Recalling that `sectheta=1/costheta,` this identity can be rewritten as

`1+tan^2theta=1/cos^2theta`

Furthermore, we know that `costheta=-3/5,` so `cos^2theta=(-3/5)^2=9/25`

Then,

`1+tan^2theta=1/(9/25)`

`1+tan^2theta=25/9`

`tan^2theta=25/9-9/9`

`tantheta=+-sqrt(16/9)=+-4/3`

So, the possible answers are `tantheta=4/3, -4/3`