Half Angle Calculator

Enter the Angle (θ):

Choose Unit: Degrees Radians

Half-Angle Functions:

sin(θ/2) = None

cos(θ/2) = None

tan(θ/2) = None

Trigonometry is a key component of mathematics, and understanding trigonometric identities can help you solve complex problems in a wide range of fields, from physics to engineering. One of the most useful identities is the half angle identity, which allows you to compute trigonometric values for half of a given angle. Instead of manually calculating the values, you can easily use our Half Angle Calculator to get quick and accurate results.

What is the Half Angle Identity?

The half angle identity is derived from the double angle identities in trigonometry and helps simplify calculations by allowing you to find trigonometric functions for half of a given angle. The half angle formulas for sine, cosine, and tangent are:

• For sine:

$$\sin\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 - \cos(\theta)}{2}}$$

• For cosine:

$$\cos\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 + \cos(\theta)}{2}}$$

• For tangent:

$$\tan\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 - \cos(\theta)}{1 + \cos(\theta)}}$$

The positive or negative sign depends on the quadrant in which the angle lies.

Why Use a Half Angle Calculator?

Using a Half Angle Calculator offers several benefits:

1. Time-Saving: Instead of manually applying the half angle identity to find values for trigonometric functions, the calculator instantly gives you the results.
2. Accuracy: The calculator eliminates human error and ensures precise trigonometric values for half of any given angle.
3. Simplifies Complex Problems: The half angle identity is often used in integration, solving equations, and simplifying trigonometric expressions. Our tool makes these tasks easier and faster.

How Our Half Angle Calculator Works

Using our Half Angle Calculator is simple:

1. Input the angle (in degrees or radians) for which you want to calculate the half angle.
2. Choose which trigonometric function (sine, cosine, or tangent) you want to calculate.
3. The calculator will instantly give you the value of the half angle for the selected function.

For example, if you want to find the half angle of sine, cosine, or tangent for a 60° angle, you simply enter the angle and the function, and the calculator will do the rest.

Why Choose Our Half Angle Calculator?

• Quick Results: Get the half angle values for sine, cosine, or tangent in just a few seconds.
• Easy to Use: With a user-friendly interface, the calculator is perfect for students, professionals, or anyone who works with trigonometry.
• Free Access: You can use the Half Angle Calculator for free, without any hidden fees or subscriptions.

Whether you’re working on a math assignment, solving complex trigonometric equations, or simply need to calculate half angles for other purposes, our Half Angle Calculator simplifies the process. Start using it today and take the hassle out of your trigonometric calculations!