Christina stared at the equation $\tan(x)=\frac{3}{7}$. “That’s interesting,” she thought. “Since $\tan x=\frac{\sin x}{\cos x}$, this must mean that $\sin(x)=3$ and $\cos(x) = 7$. But that’s impossible.”.  

1. Why is it impossible?

   Hint (a):

   What is the range of sine and cosine?

2. What is going on here?

   Hint (b):

   $\frac{0.3}{0.7}$ 

3. Solve for $x$ if $0\le x<2\pi$.

   Hint (c):

   Using a calculator, evaluate $\tan^{-1}\left(\frac{3}{7}\right)$.

   More Help (c):

   There is another solution. Use the unit circle to help you calculate the second solution.