Double Angle Calculator

Calculate Double Angle Values



Formulas

The double angle formulas are:

\[ \sin(2θ) = 2\sin(θ)\cos(θ) \]

\[ \cos(2θ) = \cos^2(θ) - \sin^2(θ) \]

\[ \tan(2θ) = \frac{2\tan(θ)}{1 - \tan^2(θ)} \]

What is a Double Angle?

The term "double angle" refers to the expression of a trigonometric value of two times an angle θ. The double angle formulas allow you to calculate the trigonometric functions of twice the angle, which are different from simply doubling the trigonometric value of the original angle. These formulas are used in various fields of mathematics and physics to simplify complex trigonometric expressions and solve problems involving periodic functions.

Example Calculation

Let's assume the following values:

Using the formula for sin(2θ):

\[ \sin(2 \times 45^\circ) = \sin(90^\circ) = 1 \]

The result is 1.