Question

What are the values of `x` that satisfy `cos^2x = 1/2`?

Answer 1

Solution is >`x in {45˚ + 360˚n, 135˚ + 360˚n, 225˚ + 360˚n, 315˚ + 360˚n}` where `n` is an integer.

Explanation:

Here's another way of doing this problem.

Take the square root of both sides.

`cosx = +- sqrt(1/2)`

`cosx = +- 1/sqrt(2)`

Now consider the `45-45-90` special triangle.

We have:

`x = 45˚`

But this is just the reference angle for the three other solutions in `0 ≤ x < 360˚`. There will also be `x = 135˚`, `x = 225˚` and `x = 315˚`.

If you want the periodic solutions, we have:

`x in {45˚ + 360˚n, 135˚ + 360˚n, 225˚ + 360˚n, 315˚ + 360˚n}` where `n` is an integer.

Hopefully this helps!