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.
