For each equation, find two solutions $0 ≤ x < 2π$, which make the equation true. No calculator should be necessary.  

1. $\cos x = −\frac { 1 } { 2 }$ 

   Hint (a):

   Recall that $\cos \left( \frac{\pi}{6}\right) = \frac{1}{2},$ so the reference angle will be $30°$.

   Step 1(a):

   In which quadrants is cosine negative? Sketch a unit circle with right triangles with $30°$ angles at the origin in the second and third quadrants. What are the circular angles?

   $x = 120°$ and $240°$

   Step 2(a):

   Now convert the angles into radians.

   $120\left(\frac{\pi}{180}\right)\ \ \ \ \ \ \ \ 240\left(\frac{\pi}{180}\right)$

   Answer (a):

   $x = \frac{2{\pi}}{3}, \frac{4{\pi}}{3}$

2. $\tan x =\frac { \sqrt { 3 } } { 3 }$ 

   Hint (b):

   See part (a).

3. $\sin x = 0$ 

   Hint (c):

   If $\sin(x) = 0$, $x = 0$.

   Partial Answer (c):

   $x = 0$

4. $\cos x =\frac { \sqrt { 2 } } { 2 }$ 

   Hint (d):

   Remember the side ratios of $45°$ right triangles.