Double Angle Calculator

Use our double angle calculator to solve trigonometry problems with double angles. Insert the angle in degrees or radians below to get started.

How to Solve Double Angles

Double angle identities express the trigonometric functions of double angles in terms of the trigonometric functions of single angles θ. They are derived from the sum or difference of angle formulas, and they are used to simplify complex expressions and prove trigonometric identities.

Calculating a double angle isn’t quite as easy as just multiplying the result of the trigonometric function by 2.

There are six double angle identities, and, just like half angles, there is a unique formula to express each one. See each formula below.

Graphic showing the double angle identities for the sine, cosine, and tangent of a double angle.

Sine of a Double Angle Formula

To calculate the sine of a double angle, you can use the following formula:

sin(2θ) = 2sin(θ)cos(θ)

Thus, the sine of 2 times an angle θ is equal to 2 times the sine of angle θ times the cosine of angle θ.

Cosine of a Double Angle Formula

To calculate the cosine of a double angle, you can use the following formula:

cos(2θ) = 1 – 2sin²(θ)

The cosine of 2 times an angle θ is equal to 1 minus 2 times the sine squared of the angle θ.

Tangent of a Double Angle Formula

To calculate the tangent of a double angle, you can use the following formula:

tan(2θ) = 2tan(θ) / 1 – tan²(θ)

Thus, the tangent of 2 times an angle θ is equal to 2 times the tangent of the angle θ divided by 1 minus the tangent squared of the angle θ.

Cosecant of a Double Angle Formula

The cosecant of a double angle is equal to the reciprocal of the sine of the double angle. To calculate the cosecant of a double angle, you can use the following formula:

csc(2θ) = 1 / 2sin(θ)cos(θ)

The cosecant of 2 times an angle θ is equal to 1 divided by 2 times the sine of angle θ times the cosine of angle θ.

Secant of a Double Angle Formula

The secant of a double angle is equal to the reciprocal of the cosine of the double angle. To calculate the secant of a double angle, you can use the following formula:

sec(2θ) = 1 / 1 – 2sin²(θ)

The secant of 2 times an angle θ is equal to 1 divided by 1 minus 2 times the sine squared of the angle θ.

Cotangent of a Double Angle Formula

The cotangent of a double angle is equal to the reciprocal of the tangent of the double angle. To calculate the cotangent of a double angle, you can use the following formula:

cot(2θ) = 1 – tan²(θ) / 2tan(θ)

The cotangent of 2 times an angle θ is equal to 1 minus the tangent squared of the angle θ divided by 2 times the tangent of the angle θ.