# How do you evaluate cos^-1 0.8217?

$\setminus {\cos}^{- 1} \left(0.8217\right) = {34.745}^{\setminus} \circ$

#### Explanation:

One can compute ${\cos}^{- 1} \left(0.8217\right)$ using calculator

$\setminus {\cos}^{- 1} \left(0.8217\right) = {34.745}^{\setminus} \circ$

Jul 15, 2018

34.7° or 325.3°

#### Explanation:

The question can be read as ..

"What angle has a cos value of $0.8217$?"

If you just need an angle in a right-angled triangle, then on a scientific calculator you would key in:

shift/alt/$2 n d F \text{ } {\cos}^{-} 1 0.8217 =$ to get an angle of 34.7°

However, if you want to include angles from 0° to 360° then we need to consider the sign and decide which quadrants we are working in.

Cos is positive in the first $1 s t \mathmr{and} 4 t h$ quadrants

The angle in the $1 s t$ quadrant is 34.7° obtained as explained above,

The angle in the $4 t h$ quadrant is 360-34.7°= 325.3°