Cosine Calculator

Use the cosine calculator to find the cos value based on a given degree or radian. Instead of numbers in radians, you can also enter radians in π combinations.

In a right triangle, the ratio of the side adjacent to the angle to the hypotenuse is called the cosine. It is called cos for short. Like sine, cosine is also one of the three major functions in trigonometric functions, the other is tangent.

The cosine formula is

cos(θ) = adjacenthypotenuse

For instance, there is a right triangle as follows

In this right triangle, the three angles are α, β and γ, where γ is the right angle. The three sides are a, b, and c, where c is the hypotenuse. Therefore, the cosines of these three angles are

cos(α) = adjacenthypotenuse = bc

 

cos(β) = oppositehypotenuse= ac

 

cos(γ) = 0

Why is the cosine of a right angle equal to 0?

The first thing to be clear is that cosine calculates ratios based on right triangles. When two right angles appear in a right triangle (90°, 90°, 0), then the triangle becomes a line segment. Therefore, the length of the adjacent side of a right angle is 0. So, the cosine of 90° is 0.

There are two ways to calculate the cosine of an angle.

The first method is that the adjacent and hypotenuse lengths are known.

For example, in a right triangle, the length of the adjacent side of angle α is 3, and the length of the hypotenuse is 5. What is the cosine of angle α?

cos(α) = adjacenthypotenuse = 45

Another way is to know the degrees or radians of the angle. At this time, you can use the cosine calculator we provided above to calculate it. Alternatively, find the cosine in degrees or radians from the cosine table (provided below). The fatal flaw of the cosine table is that it cannot list all degrees or radians. We list some commonly used cosine degrees or radians.

If you connect the cosine values of each degree, you can get a smooth curve, which is also called a cosine graph.

It can be seen from the curve that the value range of cosine is between -1 and 1. The axis of symmetry of the cosine is kπ (k is an integer). The period is the same as the sine, which is 2π.

cos(θ) = cos (θ + n * 360°) = cos (θ + n * 2π)

Also, the graph is left-right symmetrical, therefore, the cosine function is an even function.

In addition, when the angle is in different quadrants, the positive and negative values of the cosine are different. Positive in the first and fourth quadrants, negative in the second and third quadrants.

There are 3 calculations closely related to cosine.

1. Cosine derivative

The derivative of the cosine function is the negative sine function.

cos'(θ) = -sin(θ) = –oppositehypotenuse

2. Inverse cosine

The inverse of cosine is arccosine, which is used to find the angle from the cosine value. It can be represented by cos^-1 or arccos.

cos(90°) = 0

 

cos^-1(0) = arccos (0) = 90°

3. Reciprocal cosine

The reciprocal of cosine is secant, which is also a type of trigonometric function. In a right triangle, the secant of an acute angle is equal to the ratio of its hypotenuse to its adjacent side. The abbreviation is sec.

1cos(θ) = sec(θ)

There are two steps to using the cosine calculator. In the first step, enter a value. In the second step, choose the type, degrees or radians. Finally, click Calculate to get the cosine value. This cosine calculator supports the input of π, and the combination of π, such as 3π/2, 5π, etc. Fill in according to the actual situation. Please press the reset button before running a new calculation.

Like sine, cosine is a very important trigonometric function. You can remember some commonly used cosine values, but it is absolutely impossible to remember all cosine values. Therefore, you should desperately need a cosine calculator to help you, that’s why our cosine calculator exists. Hurry to try it!