Question

How do you evaluate `cos^-1 0.8217`?

Answer 1

`\cos^{-1}(0.8217)=34.745^\circ`

Explanation:

One can compute `cos^{-1}(0.8217)` using calculator

`\cos^{-1}(0.8217)=34.745^\circ`

Answer 2

`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/`2nd F" "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 `1st and 4th` quadrants

The angle in the `1st` quadrant is `34.7°` obtained as explained above,

The angle in the `4th` quadrant is `360-34.7°= 325.3°`