## Introduction to Double Angle Calculator:

Double angle calculator is a tool that helps you **compute trigonometric functions** using double angles and mathematical formulas. It is used to simplify trigonometric calculation when you are dealing with complex angles or equations.

Double angle formula calculator is a beneficial tool as it gives you instant solutions to trigonometric function problems with the help of double angle identities without taking any external help from you in the calculation.

## What is the Double Angle Formula Function?

Double angle identity is a special type of identity for the trigonometric function of **sine, cosine, or tangent** function. It helps to solve complex trigonometric problems with the help of double-angle identities of trigonometric functions.

It is a crucial formula in trigonometry that provides a systematic way for finding complicated algebraic function values without any difficulty.

## Formula of Double Angle Function:

The **formulas of double angle** functions or identities consist of sine, cosine, or tangent trigonometric functions. The formula used by the double angle calculator to compute double-angle trigonometric functions is,

**For cosine function**:

It has the double identity for both sine and cosine functions,

$$ cos(2 \theta) \;=\; cos^2 \theta - sin^2 \theta $$

**For sine function**:

The sine double identity function has the double angle value of sine,

$$ sin(2 \theta) \;=\; 2 sin \theta cos \theta $$

**For tangent function**:

In the tangent double-angle formula, you get the ratio of the tangent function over the square of the tangent function.

$$ tan(2 \theta) \;=\; \frac{2 tan \theta}{1 - tan^2 \theta} $$

## How to Calculate Double Angle Formula Function?

For **calculation** of the double-angle function, the double angle calculator uses specific trigonometric formulas to find the value of double trigonometric functions of angle. Here is a step-by-step guide for the calculation of these trigonometric functions manually.

**Step 1**:

First, understand the given trigonometric function.

**Step 2**:

Apply the double angle formula function as per your given trigonometric value function.

- For Cosine:

$$ cos(2 \theta) \;=\; cos^2 (\theta) - sin^2 (\theta) $$

- For Sine:

$$ sin(2 \theta) \;=\; 2 sin(\theta) cos(\theta) $$

- For Tangent:

$$ tan(2 \theta) \;=\; \frac{2 tan(\theta)}{1 - tan^2 \theta} $$

**Step 3**:

Perform the calculation process and simplify it to find the solution of the given trigonometric function solution.

## Solved Example of Double Angle:

The double angle formula calculator can give you an accurate solution in seconds but you need to know the manually solving method of double-angle trigonometric functions. Therefore, an **example** is given.

**Example**:

Given that tan θ = - 3/4 and θ is in quadrant Ⅱ, find the following:

$$ a. sin(2 \theta) $$

$$ b. cos(2 \theta) $$

$$ c. tan(2 \theta) $$

**Solution**:

Identify the given value for the double angle identity function,

$$ tan \theta \;=\; -\frac{3}{4} $$

Use the Pythagorean theorem to find the third side of a triangle,

$$ (-4)^2 + (3)^2 \;=\; c^2 $$

$$ 16 + 9 \;=\; c^2 $$

$$ 25 \;=\; c^2 $$

$$ c \;=\; 5 $$

For sin(2θ) double angle identity or formula is,

$$ sin (2 \theta) \;=\; 2 sin \theta cos \theta $$

Put the given value in it to get a solution,

$$ sin(2 \theta) \;=\; 2 \left( \frac{3}{5} \right) \left(-\frac{4}{5} \right) $$

$$ =\; -\frac{24}{25} $$

For cos(2θ) we know its double-angle identity,

$$ cos(2 \theta) \;=\; cos^2 \theta - sin^2 \theta $$

Put the given θ value in the above equation,

$$ cos(2 \theta) \;=\; \left(-\frac{4}{5} \right)^2 - \left(\frac{3}{5} \right)^2 $$

Simplify it to get a solution,

$$ =\; \frac{16}{25} - \frac{9}{25} $$

$$ =\; \frac{7}{25} $$

For tan(2θ) the double angle identity for the given value is,

$$ tan(2 \theta) \;=\; \frac{2 tan \theta}{1 - tan^2 \theta} $$

Substitute the given value in it and simplify it to get a solution,

$$ tan(2 \theta) \;=\; \frac{2 \left(-\frac{3}{4} \right)}{1 - \left(-\frac{3}{4} \right)^2} $$

$$ =\; \frac{ -\frac{3}{2}}{1 - \frac{9}{16} } $$

$$ =\; - \frac{3}{2} \left(\frac{16}{7} \right) $$

$$ - \frac{24}{7} $$

You can also substitute the given value in the double angle identity calculator and simplify it to get a solution directly.

## How to Use Double Angle Formula Calculator?

Double angle identities calculator has a simple layout that makes it easy to understand how to use it for evaluating the trigonometric function using the double angle formula. Here are some simple steps to understand accurately.

- Enter the angle value of the trigonometric function in the input field.
- Choose the double angle formula of a trigonometric function.
- Review the given function before hitting the calculate button to start the evaluation process in the double angles calculator.
- Click the “
**Calculate**” button to get the result of your given double angle trigonometric function problem. - If you are trying our double angle identity calculator for the first time then you can use the load example to learn more about this method.
- Click on the “Recalculate” button to get a new page for finding more example solutions to Double-angle formula problems.

## Result from Double Angle Identities Calculator:

Double-angle formula calculator gives you the **solution** of the given trigonometric function when you add the input value to it.

**Result Option**:

When you click on the result option then the double angle formula calculator gives you a solution to the given double angle formula trigonometric function problem.

**Possible Steps**:

When you click on it, this option will provide you with a solution where all the calculations of the trigonometric function double angle identities will be given.

## Useful Features of Double Angle Identity Calculator:

Double angle identities solver provides you with multiple useful features that help you evaluate the trigonometric function double angle identities and give you a solution without any difficulty. The features are:

- Double angle calculator is a
**free-of-cost**tool so you can use it for free to get the solution of trigonometric function’s double angle identity problem without paying any fee. - It is an adaptable tool that can manage various types of double angle trigonometric functions.
- Double angle formula calculator helps you to get conceptual clarity of the calculation of trigonometric function’s double angle identity.
- Double-angle formula calculator saves the time that you consume on the calculation of complex and lengthy double angle problems.
- It is a reliable tool that provides you with accurate solutions whenever you use it to calculate the double-angle trigonometric function without any error.
- Double angle identities calculator provides the solution without asking for signup which means you can use it anytime in the day.