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Half Angle Calculator

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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.

References:

  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