Question

If `sintheta=-1/3` and `pi<theta<(3pi)/2`, how do you find `tan (theta/2)`?

Answer 1

.`-3-2sqrt 2`

Explanation:

`theta` is in the 3rd quadrant, So, `tan theta > 0`..

Also, `theta/2` is in the 2nd and, therefore, `tan (theta/2) <0`.

Use `sin theta =-1/3= (2 tan (theta/2))/(1+tan^2(theta/2))`

Solving for negative root, `tan (theta/2)=-3-2sqrt 2`.