Half Angle Calculator

The half angle calculator is used to determine the trigonometric values for the angle θ/2 in terms of θ by using the expression of trigonometric functions. The half angle calculator is helpful in determining the estimated trigonometric function values. These trigonometric functions can be tricky to evaluate because of the complexity involved in the concept. This calculator comes in handy when you need to calculate half angle at one click.

In this post, we will guide you on how to calculate half angle, half angle formulas, and how to use half angle calculator.

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 angle in the given input box.
• You don’t need to specify any trigonometric function here because our calculator calculates half angle for each function.
• Press the Calculate button to see the results.

It will give you the trig half angle identities in no time at all.

Half Angle Formulas

Half angle formulas for sine, cosine, and tangent are given below:

\(sin \dfrac{\theta}{2} = \sqrt{\dfrac{1-cos \theta}{2}}\)

\(cos \dfrac{\theta}{2} = \sqrt{\dfrac{1+cos \theta}{2}}\)

\(tan \dfrac{\theta}{2} = \sqrt{\dfrac{1-cos \theta}{sin \theta}}\)

How to calculate half angle?

Half angle can be calculated using above half angle equations. Let’s understand the half angle calculation by using an example.

Example:

Find the half angle identity of trigonometric function for sin, cos, and tan for a 50-degree angle.

Follow these steps to find half angle for all trigonometric functions asked in the question.

Step 1: Write down half angle formula for sin and place values in it.

\(sin \dfrac{\theta}{2} = \sqrt{\dfrac{1-cos \theta}{2}}\)

\(= \sqrt{\dfrac{1-cos (50)}{2}}\)

\(= \sqrt{\dfrac{0.64278760968}{2}}\)

\(= 0.42262\)

So, \(sin \dfrac{\theta}{2} = 0.42262\)

Step 2: Write down half angle formula for cos and substitute values in it.

\(cos \dfrac{\theta}{2} = \sqrt{\dfrac{1+cos \theta}{2}}\)

\(= \sqrt{\dfrac{1+cos (50)}{2}}\)

\(= \sqrt{\dfrac{1+0.64278760968}{2}}\)

\(= 0.90631\)

Son, \(cos \dfrac{\theta}{2} = 0.90631\)

Step 3: Write down half angle formula for tan and substitute values in it.

\(tan \dfrac{\theta}{2} = \sqrt{\dfrac{1-cos \theta}{sin \theta}}\)

\(=\sqrt{\dfrac{1-cos (50)}{sin (50)}}\)

\(=\sqrt{\dfrac{1-cos 0.64278760968}{sin 0.76604444311}}\)

\(= 0.46631\)

So, \(tan \dfrac{\theta}{2} = 0.46631\)

If you need to calculate the double angle, you can use our double angle calculator anytime.