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What is the inverse cosine of 1/3?

1 Answer

Nov 29, 2015

$θ \approx {70.53}^{\circ}, {289.47}^{\circ}$ $theta~~70.53^@, 289.47^@$

Explanation:

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

$cos θ = \frac{1}{3}$ $costheta=1/3$
$θ = {cos}^{- 1} (\frac{1}{3})$ $theta=cos^-1(1/3)$
$θ \approx {70.53}^{\circ}$ $theta~~70.53^@$

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

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

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