# What is the inverse cosine of 1/3?

Nov 29, 2015

$\theta \approx {70.53}^{\circ} , {289.47}^{\circ}$

#### Explanation:

Since $\frac{1}{3}$ is not a ratio we can find in a special triangle, we must use a calculator:

$\cos \theta = \frac{1}{3}$
$\theta = {\cos}^{-} 1 \left(\frac{1}{3}\right)$
$\theta \approx {70.53}^{\circ}$

However, since cosine is also positive in quadrant $4$ according to the CAST rule, there is a second answer:

$\theta = {360}^{\circ} - {70.53}^{\circ}$
$\theta \approx {289.47}^{\circ}$