Solution assignment 10 Unit circle and simple formulas

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Assignment 10

Show for which values of $x$ in the interval $[0,2\pi]$ the function:

$y=\sin(3x)$

takes the value $1$ .

Solution

The function has three periods in the given interval. In one period the $sin$ -functie takes the value $1$ only once. So this will happen three times in the given interval of $x$ :

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

This yields the following values in the given interval:

$x=\displaystyle\frac{\pi}{6},\displaystyle\frac{5\pi}{6},\displaystyle\frac{9\pi}{6}$

Return to Assignments Unit circle and simple formulas

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Solution assignment 10 Unit circle and simple formulas

Assignment 10

Solution

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