Convert OnlineConvertOnline

Calculate cos−1

x= adjacent_side/hypotenuse




cos−1(x)

_

Inverse Cosine cos−1() is used to find the angle for a given ratio of the length of the adjacent side to the length of the hypotenuse, in a right angled triangle.

Formula

To find the Inverse Cosine of a given ratio: adjacent_side/hypotenuse , use the following formula.

θ = cos−1(Length_of_Adjacent_side / Length_of_Hypotenuse)

Calculating Cos Inverse

The inverse cosine (cos-1 or arccos) of a value is the angle whose cosine is the given value. It is used to find angles when the cosine value is known.

The inverse cosine of a value \( y \) is defined as:

\( \cos^{-1}(y) = \theta \)

where:

Example 1

Let's calculate the inverse cosine of 0.5:

The angle whose cosine is 0.5 is 60 degrees or \( \frac{\pi}{3} \) radians. So:

\( \cos^{-1}(0.5) = 60^{\circ} = \frac{\pi}{3} \)

Example 2

Consider another example with the value \( \frac{1}{2} \):

The angle whose cosine is \( \frac{1}{2} \) is 60 degrees or \( \frac{\pi}{3} \) radians. So:

\( \cos^{-1}(\frac{1}{2}) = 60^{\circ} = \frac{\pi}{3} \)

These examples demonstrate how to calculate the inverse cosine of a value.