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7-104.

What central angle, measured in degrees, corresponds to a distance around the unit circle of $\frac { 7 \pi } { 3 }$? Homework Help ✎

1. What other angles will take you to the same point on the circle?

2. Make a sketch of the unit circle showing the resulting right triangle.

3. Find sin$( \frac { 7 \pi } { 3 } )$, cos$( \frac { 7 \pi } { 3 } )$ and tan$( \frac { 7 \pi } { 3 } )$ exactly.

What number of degrees is equivalent to $\frac{\pi}{3}$ radians?

If you can't remember, calculate.

$\pi=180^{\circ}\ \ \ \ \ \ \ \ \frac{\pi}{3}=60^{\circ}$

Now multiply the angle by 7.

420°

The distance around the unit circle is 2π, no matter what point you start from.

$\frac{\pi}{3} \:\pm\:2\pi n$

The angle you are working with, 420°, is more than 360°. How much more?

Notice that the triangle formed is a 30°-60°-90° triangle. $\sin\left(\frac{7\pi}{3}\right)=\frac{\sqrt{3}}{2}$

$\cos\left(\frac{7\pi}{3}\right)=\frac{1}{2}$

$\tan\left(\frac{7\pi}{3}\right)=\sqrt{3}$