Home > PC3 > Chapter 7 > Lesson 7.1.2 > Problem7-25

7-25.

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

1. Why is it impossible?

What is the range of sine and cosine?

1. What is going on here?

$\frac{0.3}{0.7}$

1. Solve for $x$ if $0\le x<2\pi$.

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

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