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.
General Terms Table
To enhance user understanding, here’s a helpful table of general terms that people commonly search for:
| Term | Description |
|---|---|
| Radians | A unit of angular measurement. |
| Cosine Function | Mathematical function related to angles. |
| Square Root | Mathematical operation denoted by √. |
| Half-Angle | Half 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.
Most Common FAQs
A: To convert degrees to radians, use the formula: Radians = Degrees × (π/180).
A: No, this calculator specifically works with angles in radians. Convert non-radian angles to radians before using the calculator.
A: The ± symbol accounts for the symmetry of angles, providing both possible solutions for the half-angle.