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Question

Draw an angle with the given measure in the standard position.

2π3-\frac{2 \pi}{3}

Solution

Verified
Answered 1 year ago
Answered 1 year ago

The task is to illustrate angle 2π3-\dfrac{2\pi}{3} in standard position.

The first step is to convert 2π3-\dfrac{2\pi}{3} in degree measure.

2π3=2π3 radians(180π radians)=120-\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 2π3-\dfrac{2\pi}{3} is equivalent to 120-120^{\circ}, we can now illustrate 2π3-\dfrac{2\pi}{3} in standard position. To do this, draw the first ray (initial side) along the positive xx-axis. And considering 120=90+(30)-120^{\circ}=-90^{\circ}+(-30^{\circ}), this means that we need to draw the second ray (terminal side) 3030^{\circ} clockwise from the negative yy-axis. Note that the rotation is clockwise because the given angle is negative. 'slader'

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