Question

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

Answer 1

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°`