Cosine Calculator

To quickly get the cosine of an angle given in degrees or radians, use our Cosine Calculator. In geometry issues involving circles, right triangles, and other shapes where cos(x) may be computed, the cosine is used.

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How is the Cosine of a Number Calculated?

The cosine of an angle is calculated using the ratio of the adjacent side to the hypotenuse in a right-angled triangle. For any angle θ:

Calculation Right Triangle Method: Measure sides and compute ratio
Unit Circle Method: x-coordinate on unit circle
Series Expansion (Advanced):

Calculator/Software: Uses optimized algorithms

Cosine function calculation formula.

Key Formulas
Right Triangle Formula:

Unit Circle Formula:
cos (θ) = x - coordinate
Pythagorean Identity:
sin² (θ) + cos² (θ) = 1

Cosine function calculation Example.

Given: Right triangle with: Adjacent side = 4 Hypotenuse = 5
1: Identify sides 2: Apply formula

Find angle (optional)    θ = cos ^-1 (0.8) = 36.87°

We will now calculate the cosine function based on the formula given above. And understand cosine. Suppose you have an adjacent triangle with the adjacent side 4 units long and the hypotenuse (the longest side) 5 units long between the two. You want to find the cosine of the angle between the adjacent side (4 units) and the hypotenuse.
We first need to identify the adjacent side and the hypotenuse. Our adjacent side = 4 units, and the hypotenuse = 5 units. Now we plug these values into the formula. So cos(θ) = 4 units / 5 units. cos(θ) = 0.8 cos(θ) = 4 / 5 units. Cos (θ) = 0.8 (this may be expressed as a fraction as well). Thus, 0.8, or 4/5, is the cosine of the angle in this triangle.
If you calculate antilog based on the antilog calculation formula, but have any doubts, use our Cosine calculator to double-check the findings if you're not sure.

About the Cosine Function

Key Properties

Special Values

Understanding Cosine

Cosine Function (cos(x)): Cos(x), the cosine function, helps us to further comprehend angles. It gives an indication of the relationship between the angles of a right triangle in a way that is close to a handy calculator.

Related Trigonometric Functions: Before we delve straight to finding the cosine, we need to be acquainted with sine, sin(x), and tangent, tan(x). As a group, they form the so-called trigonometric functions triad. To learn the mysteries of angles, they join hands.

How to Calculate an Angle's Cosine: We can therefore see that if we have to find the cosine of an angle, we would not have a problem getting it. It turns out that there is an easy way to achieve all that, and here’s the formula. Take an angle and apply the cosine of it, and voilà! The result lay between -1 and 1 as a value. As the angle increases, the outcome approaches -1 or 1, and this feature is desirable while computing machine learning algorithms.

Uses for the Cosine Function: Now, you might ask why cos(x) is useful and appeals to practical purposes. Others extend it beyond purely arithmetical terms; it is applicable in almost every field of study.

Common Cosine values table

Cosine Table