Question

How do you find the solution to `25cos^2theta-4=0` if `0<=theta<360`?

Answer 1

The value of the angle `theta` is `cos^(-1)(+-2/5)`.

Explanation:

The givenequation is `25cos^2theta-4=0`.
`:.25cos^2theta=4`.

`:.cos^2theta=4/25`.

`:.cos theta=+-2/5`.

Now, the range of cosine of a certain angle is:
`-1<=costheta<=+1`.

So, the above value of cosine of the angle, `theta` is true for certain values of `theta`.

`:.theta=cos^(-1)(+-2/5)`. (Answer).