Evaluate each of the following trigonometric expressions without a calculator.

1. $\sin\left(\frac{5\pi}{3}\right)$ 

   Hint (a):

   

2. $\cos\left(-\frac{\pi}{4}\right)$ 

   Hint (b):

   

3. $\tan\left(\frac{\pi}{2}\right)$ 

   Hint (c):

   What is the slope of the line associated with an angle of $\frac{\pi}{2}$?