Arccos Calculator

What is the Arccos Function?

The arccos is an inverse trigonometric function and serves as the opposite of the cosine function. It can be presented as cos⁻¹(x), but this notation may confuse since it can also be mistaken for an exponent.

The cosine function is used to find an angle when the cosine ratio is known. In a right triangle, the cosine ratio is the length of the adjacent side divided by the hypotenuse.

The domain of the arccos function is between -1 and 1, and its outputs (angles) lie within 0° to 180°.

Here are some useful arccos properties and identities in trigonometry:

•       cos(arccos(x)) = x
•       arccos(α) + arccos(β) = arccos (αβ − √((1−α²) (1−β²)))
•       sin(arccos(x)) = √(1−x²).

How to calculate the arccosine of a number?

The easiest way to find the arccosine of a number is to use an online arccosine calculator. But if you want to do it manually, then keep in mind the following procedure.

Follow the below mentioned steps to calculate the inverse cosine:

• Ensure the input value is between -1 and 1.
• Use the formula θ = cos−1(x) and put the value in the place of x.
• Find the value of the angle in the table or use an arccos calculator whose cosine equals the given value.
• Express the angle in degrees (0°–180°) or radians (0–π).

Example:

Find arccos (0.5)

Solution:

According to the definition of arccos

arccos(x)=θ such that cos(θ)=x and       0≤θ≤π

Substitute the value

We want θ=arccos (0.5).

So,

cos(θ)=0.5

We know that:

cos (60∘) = 0.5 or in radians: cos (π / 3) = 0.5

arccos (0.5) = π / 3(in radians) or 60∘ (in degrees).

Common Arccos Values Table

Here is a table of some common arccos values in degrees and radians: