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Question

# Draw an angle with the given measure in the standard position.$-\frac{2 \pi}{3}$

Solution

Verified

The task is to illustrate angle $-\dfrac{2\pi}{3}$ in standard position.

The first step is to convert $-\dfrac{2\pi}{3}$ in degree measure.

$-\dfrac{2\pi}{3}=-\dfrac{2\cancel{\pi}}{3}\cancel{\text{ radians}}\left(\dfrac{180^{\circ}}{\cancel{\pi}\cancel{\text{ radians}}}\right)=-120^{\circ}$

Since we already know that $-\dfrac{2\pi}{3}$ is equivalent to $-120^{\circ}$, we can now illustrate $-\dfrac{2\pi}{3}$ in standard position. To do this, draw the first ray (initial side) along the positive $x$-axis. And considering $-120^{\circ}=-90^{\circ}+(-30^{\circ})$, this means that we need to draw the second ray (terminal side) $30^{\circ}$ clockwise from the negative $y$-axis. Note that the rotation is clockwise because the given angle is negative. ## Recommended textbook solutions #### Algebra 2

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