You should come up with the substitution `sin theta = y` such that:

`2y^2 - 7y + 3 = 0`

You need to use quadratic formula to find `y_(1,2)` such that:

`y_(1,2) = (7+-sqrt(49 - 24))/4`

`y_(1,2) = (7+-sqrt25)/4 =gt y_(1,2) = (7+-5)/4`

`y_(1) = 3 ; y_(2) = 1/2`

You need to find `theta` such that:

`sin theta = 3` is a contradiction since the values of sine function are not larger than 1.

`sin theta = 1/2 =gt theta = arcsin(1/2)`

`theta= 30^o` and `theta = 150^o`

Notice that the values for theta are in quadrants 1 and 2 since the values of sine function are positive in these quadrants.

**Hence, the solutions to equation are `theta = 30^o` and `theta = 150^o` .**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now