Determine the exact value of each of the following trigonometric expressions without using a calculator.  

1. $\cos\left(\frac{7\pi}{6}\right)$ 

   Hint (a):

   Draw a unit circle with reference angle.

   

2. $\sin\left(\frac{3\pi}{2}\right)$ 

   Hint (b):

   Follow the hint in part (a).

3. $\tan\left(\frac{3\pi}{2}\right)$ 

   Hint (c):

   What is the slope of the line associated with this angle?

4. $\tan\left(\frac{2\pi}{3}\right)$ 

   Hint (d):

   Follow the hint in part (a).