# Math Help - acute angle

1. ## acute angle

find acute angle x such that

$\cos x+\cos 2x+\cos3x=-0.5$

2. By writting $\cos x=\frac{e^{ix}+e^{-ix}}2$ you can turn the original equation into a nice one.

3. Alternatively, note that the roots of the complex equation $z^7-1=0$ are

$z\ =\ 1,\ \cos{\frac{2\pi}{7}}\pm\mathrm{i}\,\sin{\frac{2\pi }{7}},\ \cos{\frac{4\pi}{7}}\pm\mathrm{i}\,\sin{\frac{4\pi }{7}},\ \cos{\frac{6\pi}{7}}\pm\mathrm{i}\,\sin{\frac{6\pi }{7}}$

Sum the roots and equate to 0.