Question #a070e

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Answer 1 · 2017-02-26T22:40:05

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

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 $pm$ .