# What is \cos ^{-1}(.60)?

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#### Explanation

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#### Explanation:

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4
Jan 1, 2017

cos^-1 (0.6)= 53.1°

#### Explanation:

Note that ${\cos}^{-} 1$ does not mean $\frac{1}{\cos}$ as we are used to in algebra.

${\cos}^{-} 1$ is the notation used for arc-cos.

Cos 30° = 0.866 " "hArr" "cos^-1(0.866) = 30°

In this case ${\cos}^{-} 1 \left(0.60\right)$ is asking the question..

"Which angle has a $C o s$ value of 0.60?"

The only way to determine this is with a calculator or tables.
Using a graph is possible, but not accurate enough.

Depending on which calculator you have, the following are possible key presses:

D.A.L. calculators:

shift cos^-1 (0.6) =" larr ( ) might not be needed on some models

The answer will be 53.1°

Or $0.6 \text{ shift" cos^-1" } \leftarrow =$ sign not needed, the answer $\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .}$appears immediately

The answer will be 53.1°

Note that this is only the acute angle, the 1st quadrant angle.
In the 4th quadrant, Cos 306.9° = 0.6

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