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# Cosine Calculator

Angle (θ)

Table of Content
 1 Cosine Formula: 2 Law of Cosine: 3 How to Find Cosine of an Angle? 4 Graph of Cosine: 5 Table for Cosine: 6 What is Cosine used for? 7 What is Cosine used for in Real Life? 8 Why is Cos Positive? 9 Why do we need Trigonometric Functions
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The online free cosine calculator helps in calculating the cosine value of the given angle in degrees, radians, mili-radians, and π radians. Here we have much more for you including how to find a cosine curve, some elementary cosine law, and much more! So, let’s initiate with the general definition of cosine.

## What is Cosine in Math?

In mathematics, trigonometric functions are real functions that related to a right angle triangle with two sides length and one hypotenuse. Assuming a right-angled triangle, the cos(x) function of an angle is defined as the length of the adjacent side divided by the length of the hypotenuse. The value of this trigonometric function cos(x) for the given angle can be calculated by using a cosine calculator. Furthermore, the range of cosine is $$-1 ≤ cos ≤ 1$$, and the period of cosine is equal to $$2π$$.

### Cosine Formula:

The formula for the cosine function is:

$$cos(θ) = \frac {\text{adjacent } b}{\text{hypotenuse } c}$$

To solve cos manually, just use the value of the adjacent length and divide it by the hypotenuse.

In addition, an Online Secant Calculator uses to find the secant of the given angle in degree, radian, or the π radians.

## How to Find Cosine of an Angle?

As the cosine of angle θ, is the ratio between the adjacent length of the angle and the hypotenuse so apply the following formula to find cosine of an angle:

$$cos(α) = \frac{b}{c}$$

#### Example 1:

Calculate value of cos θ?

Solution:

If the length of the adjacent side is 12 and the value of the hypotenuse is 6 then according to cos formula:

$cos θ = \frac{12}{6} = 2$

#### Example 2:

Find the values of Cos 60°.

Solution:

By using the Cosine table or calculator,

$Cos 60°= \frac{1}{2} = 0.5$

You may also use a cosine calculator for error-free calculation.

## Graph of Cosine:

A cosine graph represents a repeating up/down the curve. This curve is known as a cosine wave. While plotting a graph always remember:

• Once the curve starts it will decrease first to a value of -1.
• After decreasing, the curve will increase to a value of 1, and then the whole process will continue open-endedly.

## Table for Cosine:

The value of cosine function for all the common angles can be quickly picked up from the following table for fast calculations:

 Degrees(°) Radians cos (x) 180° π -1 150° 5π/6 -√3/2 135° 3π/4 -√2/2 120° 2π/3 -1/2 90° π/2 0 60° π/3 1/2 45° π/4 √2/2 30° π/6 √3/2 0° 0 1

How does Cosine Calculator Work?

This cos calculator illustrates that how to find a cosine quickly just in two steps.

Moreover, an Online Sine Calculator helps you to determine the sine trigonometric values for the given angle in degrees, radians, or the π radians.

### Input:

• Enter the value of the given angle θ.
• Click the “Calculate” Button

### Output:

This calculator will determine the following output by using to cosine formula and table.

• The value of cosine either in radians, degrees, m radian, or pi (π) radians will be displayed.
• It displays answers in the simplest form.
• The unit of angle will be delivered the same as your input

## FAQs:

### What is Cosine used for?

If you have a triangle and want to relate all of its three sides to one angle, then you have to apply the Cosine Rule. However, to find the length of a side, you must know the other two sides as well as the opposite angle.

### What is Cosine used for in Real Life?

The trigonometric function cosine is commonly used to find the location and to calculate distances in the GPS system of smartphones and IOS devices. Furthermore, it can also be used in space flight and ballistic trajectories.

### Why is Cos Positive?

Cos is labeled as positive for the reason that θ will always be measured from the positive x-axis.

### Why do we need Trigonometric Functions?

Almost all the trigonometric skills provide support to the students who are working on complex angles and dimensions in a comparatively short time. They can be implemented in many other fields as well. such as:

• Architecture
• Engineering
• Sciences
• Mathematics etc.

## Conclusion:

Well, thanks to the cosine calculator that provides its support without any cost to calculate the value of cosine function whenever we want.  Additionally, for all of those students and professionals who are enthusiastic to learn new things and want to acquire more knowledge about trigonometry, it is a great choice. So just get your hands on this calculator to enjoy its reimbursements.

## Reference:

From the source of Wikipedia: Right-angled triangle, Unit-circle, Algebraic values.

From the source of  Study dot com: The Cosine Function, Cosine and Its Relation to a Unit Circle.

From the source of Clark Uni: Right triangles and Cosines, The Pythagorean identity for sines and cosines, Cosines for special common angles.