Enter the angle in degrees or radians into the calculator to determine the double angle.

Double Angle Formula

The double angle formula is a trigonometric identity that expresses a trigonometric function of twice an angle in terms of the function of the angle itself. The formula can be used to simplify the computation of trigonometric functions for larger angles. The double angle formula for sine, cosine, and tangent are given as:

sin(2θ) = 2sin(θ)cos(θ)
cos(2θ) = cos²(θ) - sin²(θ) = 2cos²(θ) - 1 = 1 - 2sin²(θ)
tan(2θ) = (2tan(θ)) / (1 - tan²(θ))

These formulas are useful in various applications of trigonometry, including solving trigonometric equations, proving identities, and simplifying expressions.

Understanding Double Angle Formula

The double angle formula plays a crucial role in the field of trigonometry. It’s particularly helpful when dealing with integrals and derivatives of trigonometric functions, as well as in the solution of trigonometric equations. Understanding and applying the double angle formula can simplify complex trigonometric problems.

How to Use the Double Angle Formula Calculator?

To use the Double Angle Formula Calculator, follow these steps:

  1. Choose between the basic calculator (for angles in degrees) or the advanced calculator (for angles in radians).
  2. Enter the given angle in the appropriate field.
  3. Click the “Calculate” button to compute the double angle.
  4. The result will be displayed in the respective field as the double angle value.
  5. If needed, click the “Reset” button to clear the fields and start a new calculation.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Angle = 30°

Double Angle = 60°

FAQ

1. What is the double angle formula?

The double angle formula is a set of trigonometric identities that express the function of twice an angle in terms of the function of the angle itself.

2. How do you calculate the double angle?

You can calculate the double angle using the formulas: sin(2θ) = 2sin(θ)cos(θ), cos(2θ) = cos²(θ) – sin²(θ), and tan(2θ) = (2tan(θ)) / (1 – tan²(θ)).

3. When should I use the double angle formula?

Use the double angle formula when you need to simplify trigonometric expressions, solve trigonometric equations, or work with integrals and derivatives involving trigonometric functions.

4. Can this calculator be used for