# How do you solve 8\sin ^ { 2} \theta + 17\sin \theta + 9= 0?

Apr 27, 2017

$\theta = - 90$

#### Explanation:

Let $\sin \theta = a$

So we can write

$8 {a}^{2} + 17 a + 9 = 0$

or

$8 {a}^{2} + 8 a + 9 a + 9 = 0$

or

$8 a \left(a + 1\right) + 9 \left(a + 1\right) = 0$

or

$\left(a + 1\right) \left(8 a + 9\right) = 0$

or

$a + 1 = 0$

or

$a = - 1$

or

$\sin \theta = - 1$

or

$\theta = - 90$--------Ans1

or

$8 a + 9 = 0$

or

$8 a = - 9$

or

$a = - \frac{9}{8}$

or

$\sin \theta = - \frac{9}{8}$

or

$\theta = I n v a l i d$

So we get $\theta = - 90$