What is the measure in degrees of a central angle measuring $\frac { 7 \pi } { 3 }$ radians?

1. What other angles correspond to the same point on the circle?

   Hint (a):

   The distance around the unit circle is $2π$, 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. What are 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):

   $\text{sin}(\frac{7\pi}{3})=\frac{\sqrt{3}}{2}$                       $\text{cos}(\frac{7\pi}{3})=\frac{1}{2}$                      $\text{tan}(\frac{7\pi}{3})={\sqrt{3}}$