# How do you use a calculator to evaluate cos^-1 0.24 in both radians and degree?

Jun 2, 2018

76.113$\circ$ and/or $\frac{76133 \pi}{180000}$

#### Explanation:

First i would get the degree by doing ${\cos}^{-} 1 \left(0.24\right)$ in a calculator to get 76.113$\circ$
This is $76.133$ out of $360$ which is $\frac{76.133}{360}$
Radians is out of $\tau$ or $2 \pi$ To find out radian multiply the fraction by $\tau$ or $2 \pi$ to get:
$\frac{76.133}{360} \cdot 2 \pi = \frac{152.266 \pi}{360} = \frac{76133 \pi}{180000}$

Jun 3, 2018

$x = {76}^{\circ} , \mathmr{and} \frac{19 \pi}{45}$
$x = {284}^{\circ} , \mathmr{and} \frac{71 \pi}{45}$

#### Explanation:

${\cos}^{-} 1 \left(0.24\right)$ --> arccos (0.24)
Calculator and unit circle give -->
cos x = 0.24 -->
arc $x = \pm {76}^{\circ}$
For $\left(0 , {360}^{\circ}\right)$ the answers are:
$x = {76}^{\circ}$ and
$x = {284}^{\circ}$ (co-terminal to $- {76}^{\circ}$)
$x = {76}^{\circ}$ --> $x = \frac{76 \pi}{180} = \frac{19 \pi}{45}$.
$x = {284}^{\circ}$ --> $x = \frac{284 \pi}{180} = \frac{71 \pi}{45}$