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Half-Angle Formula Calculator Online

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The Half-Angle Formula Calculator is a powerful tool that allows users to find the half-angle (θ/2) of a given angle in radians. This formula is expressed as:

Half Angle (θ/2) = ±√[(1 - cos(θ)) / 2]

Here, θ represents the original angle in radians. Users can easily determine the half-angle by substituting the value of θ into the formula. For example, if the original angle is θ = 60 degrees, it needs to be converted to radians first (θ = π/3 radians) before applying the formula.

Formula Breakdown of Half-Angle Formula Calculator

Let’s break down the components of the formula:

  • Half Angle (θ/2): The result we are seeking.
  • ±: Indicates that there are two possible solutions, considering the symmetry of angles.
  • √: Represents the square root operation.
  • cos(θ): The cosine of the original angle.
  • (1 – cos(θ)) / 2: The core expression within the square root, providing the basis for the calculation.
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General Terms Table

To enhance user understanding, here’s a helpful table of general terms that people commonly search for:

TermDescription
RadiansA unit of angular measurement.
Cosine FunctionMathematical function related to angles.
Square RootMathematical operation denoted by √.
Half-AngleHalf of a given angle, calculated using the formula.

Example of Half-Angle Formula Calculator

Let’s consider an example to illustrate the application of the Half-Angle Formula:

Suppose we have an original angle θ = 45 degrees. To find the half-angle, we convert it to radians (θ = π/4 radians) and substitute it into the formula:

Half Angle (θ/2) = ±√[(1 - cos(π/4)) / 2]

Calculating this expression will yield the desired result for the half-angle.

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Most Common FAQs

Q: How do I convert degrees to radians?

A: To convert degrees to radians, use the formula: Radians = Degrees × (π/180).

Q: Can I use this calculator for non-radian angles?

A: No, this calculator specifically works with angles in radians. Convert non-radian angles to radians before using the calculator.

Q: Why are there two solutions in the formula?

A: The ± symbol accounts for the symmetry of angles, providing both possible solutions for the half-angle.

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