How many degrees are in 6.8 counterclockwise rotations and find cos (cos^-1 2/5) in exact form.

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If this question is asking for `cos (cos^-1(2/5))`  then the answer is a matter of understanding the difference between cosine and inverse cosine.

Cosine represents a ratio between two lengths. This ratio will always be the same for a given angle in a right triangle. Thus, the consine of an ...

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If this question is asking for `cos (cos^-1(2/5))`  then the answer is a matter of understanding the difference between cosine and inverse cosine.

Cosine represents a ratio between two lengths. This ratio will always be the same for a given angle in a right triangle. Thus, the consine of an angle, θ, will give us a ratio.

The inverse cosine works in the opposite direction: it takes a ratio, and tells us what angle provides that ratio in a right triangle.

Therefore, `cos^-1(2/5)` will tell us the angle. However, the question is asking for the cosine of this angle.

The cosine of this angle is 2/5.

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Each counterclockwise rotation is `(+360˚)`

`6.8*360 = 2448`

6.8 counterclockwise rotations equals 2448˚.

Find `cos^(-1) (2/5).`

`cos^-1 = 66.422` ˚

Approved by eNotes Editorial Team