Solution assignment 02 Trigonometric equations

Solve:

$\cos(x)=0$

$\cos(x)=-1$

For the first equation we have:

$x=\displaystyle\frac{\pi}{2}+2k\pi, k=0, \pm1, \pm2, ...$ or

$x=\displaystyle\frac{3\pi}{2}+2k\pi, k=0, \pm1, \pm2, ...$

We can also write these solutions in one line:

$x=\displaystyle\frac{\pi}{2}+k\pi, k=0, \pm1, \pm2, ...$

For the second equation we have:

$x=\pi+2k\pi, k=0, \pm1, \pm2, ...$

The unit circle shows that the value $-1$ occurs only once per period.