Answer
$117.8^{\circ}$
Work Step by Step
First, ensure that your calculator is in radians.
On your graphing calculator, press the following sequence of buttons:
1. COS$^{-1}$
2. (
3. -.4664
4. )
5. ENTER
Therefore, $cos^{-1}(-.4664)=2.056$ radians. Then, convert this number to degrees by multiplying by $\frac{180}{\pi}$.
$2.056radians=(2.056(\frac{180}{\pi}))^{\circ}\approx117.8^{\circ}$.