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

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

   Hint (a):

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

   Answer (a):

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

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

   Hint (b):

   The angle you are working with, $420^\circ$, is more than $360^\circ$. How much more?

   Answer (b):

   

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

   Hint (c):

   Notice that the triangle formed is a $30^\circ-60^\circ-90^\circ$ triangle.

   Answer (c):

   $\sin\left(\frac{7\pi}{3}\right)=\frac{\sqrt{3}}{2}$

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

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