Half Angle Formula Calculator

To find the value of half-angle, enter the value of the original angle in radians or degrees in the half-angle formula calculator

Half Angle Identities

  • Enter pi instead of π
    in case of radians

Half angle identity calculator 

This half Trig identities solver is used to find the sine, cosine, or tangent of half a given angle based on the trigonometry identity formula.

What is a half-angle?

Half angle means the value of trigonometric angle divided by 2. These angles are computed through special formulas. Representations for these angles are

  • Sin(y/2)
  • Cos(y/2)
  • Tan(y/2)

Like double angles, half-angles are used for simplification purposes. 

Half-angle formula: 

The half-angle formulas are different for every trigonometric identity.

For sine, the formula used is:

Sin (y/2)= √1 - Cosy/2

For cos:

Cos (y/2)= √1 + Cosy/2

And lastly, for tan is,

Tan (y/2)= √1 - Cosy/1 + Cosy

How to find a half-angle?

To learn how to find a half-angle, look at this example.


Find the half-angle of tan 30°.


Step 1: Write the formula of tan(y/2).

 Tan (y/2)= 1 - Cosy/1 + Cosy

Step 2: Put the value in the formula.

 Tan (y;2)= √1 - Cos(30) / 1 + Cos(30)

 Tan (y/2)= √1 - 0.85 / 1 + 0.85

Tan (y/2) = 0.2679