Half Angle Identity Calculator

Explore trigonometric half-angle identities with ease. Calculate sin(θ/2), cos(θ/2), and tan(θ/2) using this interactive tool.

Enter Angle:

Select Unit:

Choose Function:

Result:

Value of (θ/2):

Visualization

Understanding Half Angle Identities

Half-angle identities are trigonometric formulas that relate the trigonometric functions of an angle θ/2 to those of angle θ. They are particularly useful when you need to find trigonometric values of angles that are half of standard angles.

The key half-angle identities are:

Sine Half-Angle: $$\sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1 - \cos(\theta)}{2}}$$
Cosine Half-Angle: $$\cos(\frac{\theta}{2}) = \pm\sqrt{\frac{1 + \cos(\theta)}{2}}$$
Tangent Half-Angle: $$\tan(\frac{\theta}{2}) = \frac{\sin( heta)}{1 + \cos(\theta)} = \frac{1 - \cos(\theta)}{\sin(\theta)}$$

Use this calculator by entering your angle, selecting the unit (degrees or radians), and choosing the trigonometric function you want to calculate. The visualization provides a graphical representation of the angle and its half angle on the unit circle.