Question

Question #a070e

Answer 1

`cos x = 1/2 pm sqrt( 3)/2`

Explanation:

Is it: `1 - sin^2 x - cos x = 1/2` ??

If so, use the Pythagorean Identity `sin^2 t + cos^2 t = 1` to get:

`1 - ( 1 - cos^2 x) - cos x = 1/2`

Use algebra to turn that into a Quadratic:

`cos^2 x - cos x - 1/2 = 0`

This now looks like : `z^2 - z - 1/2 = 0`, right?!

So you can use the Quadratic Formula or just complete the square as follows:

`(z - 1/2 )^2 - 1/4 - 1/2 = 0`

`(z - 1/2 )^2 = 3/4`

`z = 1/2 pm sqrt( 3)/2`

`implies cos x = 1/2 pm sqrt( 3)/2`

Put that into your calculator. You won't get solutions for the plus bit of the `pm`.