 # Half Angle Calculator

## Half Angle Formula

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

sin (θ / 2) = √ 1 – cos θ / 2

cos (θ / 2) = √ 1 + cos θ / 2

tan (θ / 2) = 1 – cos θ / sin θ

The half angle calculator is used to measure the trigonometric values for half angle (θ/2). This 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.

## 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 degree the text box.
• 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 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 half angle for sin, cos, 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.

1. What Are Half Angle Identities?. Sciencing.com
2. Half-Angle Formulas -- from Wolfram MathWorld.
3. How to Use Half-Angle Identities to Evaluate a Trig Function - dummies.com
4. Bourne, M. (2020). 4. Half Angle Formulas. Intmath.com