Double Angle Calculator - Calculator Academy

Use this calculator to determine the double angle equivalent of a given angle theta, and the trigonometric function of your choice. This calculator can also determine the original angle given any of the double angle values.

Double Angle Formula

The term double angle refers to the expression of a trigonometric value of two times and angle θ. The following formulas can be used to calculate the double angle.

sin(2θ)

cos(2θ)

tan(2θ)

To calculate the double angle values, simply take the sine, cosine, and tangent values of 2 times the angle.

Some additional equivalent formulas can be seen below. The reason that these formulas are special is that doubling the angle of a trigonometric function does not, in fact, yield double the result.

Using the calculator above, enter the angle theta ( θ ) and select the sine, cosine, or tangent depending on which trigonometric function you want to use.

How to calculate a double angle

Double angles are used in trigonometry to express the values of trigonometric functions in terms of doubling their angle. You might be thinking to yourself, ok, that’s simple, I need to enter twice the angle. You are true with respect to using this calculator, but what you may be missing is that these values can be calculated through the formulas above. These are all equivalent formulas.

Let’s look at an example. Let’s say you have a value of .45, and you are told it’s the double angle sine value you, so how do you calculate what the angle is? To do that, you need to use one of the formulas above and solve for theta. The simplest way is to probably use the sine/cosine equivalent and solve for theta.

Triple Angle Formulas

As you may have guessed, there are also formulas for determining the triple angle value of a trigonometric function. Those can be seen below.