Solution assignment 02 Trigonometric equations

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Assignment 2

Solve:

\cos(x)=0

\cos(x)=-1

Solution

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.

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