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

Question

asked May 7, 2022 135k views

1 Answer

Arjun Mehta · Answer 1 · 2022-05-12T11:47:25+0000

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 = -(1)/(2) and
x = (2)/(3) .

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