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Half Angle Calculator

Half Angle Calculator

Calculate With:

Angle (x)

 

sin(x)

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An online half angle calculator allows you to determine half-angle for sin (θ/2), cos (θ/2), and tan (θ/2) for the given angle. Also, this half angle formula calculator helps in computing the basic trigonometric values with half angle formulas and overcome the complications in trigonometric functions. Here we’ll guide you on how to find half angle of trigonometric functions by using half angle trig identities and much more.

Let’s begin with some basics!

What is Half-Angle?

Half angle formulas are used to merge the relational trigonometric expressions. These formulas can be derived from double angle identities and utilized to determine the half-angle identity of sine (sin), cosine (cos), and tangent (tan). The online half angle calculator is useful in calculating the estimated trigonometric functions.

Half Angle Identities:

$$ Sin (θ / 2) = \sqrt{ 1 – cos θ/ 2}$$

$$ Cos (θ / 2) = \sqrt{ 1 + cos θ / 2}$$

$$ Tan (θ / 2) = \sqrt {1 – cos θ /sin θ}$$

Or

$$ Tan (θ / 2) = (sin θ /1 – cos θ) $$

However, an Online Double Angle Calculator allows you to determine all basic double angle identities of the given angle.

How to Calculate Half-Angle?

Half angle can be determined by using the above half angle formulas. Here’s an example of half angle identities for better understanding.

Example:

Find the half angle for sine, cosine, and tangent for a 60-degree angle.

To calculate half angle, you can use half angle calculator otherwise follow these steps:

  1. Put the given angle value in the half angle formula for sin.

$$ Sin (θ / 2) = \sqrt{ 1 – cos θ} / 2 $$

$$ = \sqrt {1-cos(60)} / 2 $$

$$ = \sqrt {1 – (0.5)} / 2 $$

$$ = 0.866 $$

$$ Sin (θ / 2) = 0.866 $$

  1. Plug the given angle value in the half angle formula for cos.

$$ cos θ/2 = \sqrt{1 + cos θ} / 2 $$

$$ = \sqrt{1 + cos (60)} / 2 $$

$$ = \sqrt{1 + (-0.5)} / 2 $$

$$ = 0.5 $$

$$ cos θ/2 = 0.5 $$

  1. Add the value of given angle in the half angle formula for the tan.

$$ tan θ/2 = 1 – cos θ / sin θ $$

$$ = 1 – cos (60) / sin (60) $$

$$ = 1 – (-0.5) / (0.866) $$

$$ = 1.73205 $$

$$ tan θ/2 = 1.73205 $$

However, The Online Pythagorean Theorem Calculator allows you to determine the length of any missing sides of a right triangle.

How Half Angle Calculator Works?

An online Half angle formula calculator evaluate half angle identities by follow these steps:

Input:

  • First, choose an option from the drop-down list which you want to calculate.
  • Now, substitute the values in relevant fields.
  • Hit the calculate button to see the results.

Output:

  • The free online calculator provides a table with the value of half-angle functions.
  • Then, display half angle formulas for trigonometric functions.
  • Provide step-by-step calculations for entered angle value.

FAQ:

What are the uses of trigonometry in real life?

Trigonometry is used in aviation and naval industries. It also used in cartography for the creation of maps, in satellite systems, and the roof in buildings.

How trigonometric functions discovered?

The first table of chords was developed by the Greek mathematician Hipparchus in the year of 140 BC. Although these tables for chords have not survived for long time, it is claimed that 12 books of tables of chord were written by mathematician Hipparchus. These books makes Hipparchus the founder of trigonometry functions.

Conclusion:

Use an online half angle calculator to find the trigonometric values for angle θ/2 in the terms of θ with the expression of different trigonometric functions. The half angle identity calculator is beneficial for finding the estimated trigonometric function values. These trigonometric functions and identities can be tricky to calculate because of the complexity mixed up in the concept. This free online calculator comes in handy when you want to find half angle at one click.

Reference:

From the source of Wikipedia: half-angle formulae, Sine, cosine, and tangent of multiple angles, Linear combinations.

From the source of Interactive Mathematics: Half Angle Formula – Sine, Cosine, Tangent, Evaluating and Proving Half-Angle Identities.

From the source of Study dot com: Half Angles: A Flight School Analogy, Rules for Determining the Correct Sign, Listing the Half-Angle Formulas.