# Half Angle Calculator

To use half angle formula calculator, enter angle in degrees or radians, select sin, cos, or tan, and hit calculate button

## Half Angle Formula Calculator

Half angle calculator is used to measure the trigonometric values for half angle (θ/2). This half angle identity calculator aids in evaluating the trigonometric value by using the half angle formulas.

Our half angle formula calculator reduces the complication in the trigonometric functions by automating the process.

## Half Angle Formula

The following formulas are half-angle formulas for sin, cos, and tan respectively.

For sine

sin (θ / 2) = (√ 1 – cos θ / 2)

For cosine

cos (θ / 2) = (√ 1 + cos θ / 2)

For tangent

tan (θ / 2) = (1 – cos θ / sin θ)

or

tan (θ / 2) = (sin θ / 1 – cos θ)

or

tan (θ / 2) = (√ 1 – cos θ / 2 / 1 + cos θ)

## How to use half angle calculator?

To use our half angle formula calculator for evaluating half angle for trigonometric identities, follow these steps:

• Enter the θ angle in degrees or radians.
• Click on the trigonometric function you want to calculate, i.e., sin, cos, or tan.

You can use our double angle calculator if you need to calculate the double angle.

## How to calculate a half angle?

Let’s calculate half angle step by step with an example.

#### Example:

Calculate the half angle for sin, cos, and tan for a 120-degree angle.

To find a half angle for sin, cos, and tan, follow the steps below:

Step 1: Substitute the given angle in the half-angle formula for sine.

sin θ/2 = √1 – cos θ / 2

= √1 – cos (120) / 2

= √1 – (-0.5) / 2

= 0.866

sin θ/2 = 0.866

Step 2: Place the given angle in the half angle formula for cosine.

cos θ/2 = √1 + cos θ / 2

= √1 + cos (120) / 2

= √1 + (-0.5) / 2

= 0.5

cos θ/2 = 0.5

Step 3: Substitute the given angle in the half-angle formula for the tangent.

tan θ/2 = 1 – cos θ / sin θ

= 1 – cos (120) / sin (120)

= 1 – (-0.5) / (0.866)

= 1.73205

tan θ/2 = 1.73205

The half angle calculator exact value will be the same as calculated by the above formulas.

### References:

1. What Are Half-Angle Identities?. Sciencing.com
2. How to Use Half-Angle Identities to Evaluate a Trig Function - dummies.com
3. Bourne, M.4. Half Angle Formulas. openstax.org