Question

Solve the equation 3 cos 2 theta + sin theta = 1 for values of theta from 0 degrees to 180 degrees​

Answer 1

Step-by-step explanation:

Recall that

$\cos{2\theta} = 1 -2\sin^2\theta$

so we can write our original equation as

$3 - 6\sin^2{\theta} + \sin{\theta} = 1$ or

$6\sin^2{\theta} - \sin{\theta} - 2 =0$

Let $x = \sin{\theta}$ so our equation becomes

$6x^2 - x - 2= 0$

which gives us two roots: $x = -\frac{1}{2}$ and $x = \frac{2}{3}$.

This is equivalent to $\theta = 150°$ and $\theta = 41.8°$