Question

What values for `theta` for `( 0 ≤ theta ≤ 2pi)` satisfy the equation `3sin theta = sin theta -1`?

Answer 1

The Solns. in `[0,pi]` are `7pi/6, and, 11pi/6`.

Explanation:

`3sintheta=sintheta-1 rarr 2sintheta=-1 rArr sintheta=-1/2`

`:. sintheta=sin(pi+pi/6) rArr theta=7pi/6`.

Also, `sintheta=-1/2=sin(2pi-pi/6) rArr theta=11pi/6`.

Thus, the Solns. in `[0,pi]` are `7pi/6, and, 11pi/6`.