Solution assignment 05 Trigonometric equations

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Assignment 5

Solve the following equatio:

$\sin(x)=\cos(\displaystyle\frac{\pi}{3})$

Solution

In the left- and right-hand side there are different functions, a $\sin$ - and a $\cos$ -function (actually the latter one is a constant). In order to solve the equation we write:

$\sin(x)=\cos(\displaystyle\frac{\pi}{2}-x)$

getting the equation:

$\cos(\displaystyle\frac{\pi}{2}-x)=\cos(\displaystyle\frac{\pi}{3})$

and thus we get the following solutions:

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

$x=\displaystyle\frac{1}{6}\pi+2k\pi, k=0, \pm1, \pm2, ...$

or:

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

$x=\displaystyle\frac{5}{6}\pi+2k\pi, k=0, \pm1, \pm2, ...$

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Solution assignment 05 Trigonometric equations

Assignment 5

Solution

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