Compound Angle Formula Calculator

Compound Angle Formulas:

\[ \sin(A \pm B) = \sin A \cos B \pm \cos A \sin B \] \[ \cos(A \pm B) = \cos A \cos B \mp \sin A \sin B \] \[ \tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B} \]

Angle A:

degrees

Angle B:

degrees

Operation:

Trig Function:

Result:

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From:	To:

1. What Are Compound Angle Formulas?

Compound angle formulas are trigonometric identities that express trigonometric functions of the sum or difference of two angles in terms of functions of the individual angles. These formulas are fundamental in trigonometry and have wide applications in mathematics, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the standard compound angle formulas:

\[ \sin(A \pm B) = \sin A \cos B \pm \cos A \sin B \] \[ \cos(A \pm B) = \cos A \cos B \mp \sin A \sin B \] \[ \tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B} \]

The calculator converts input angles from degrees to radians, applies the appropriate formula based on your selection, and returns the trigonometric value.

3. Applications of Compound Angle Formulas

Details: Compound angle formulas are used in wave physics, electrical engineering (AC circuit analysis), mechanical engineering (vibration analysis), computer graphics (rotation transformations), and navigation systems.

4. Using the Calculator

Tips: Enter two angles in degrees, select whether you want to add or subtract them, and choose the trigonometric function you want to calculate. The result will be a unitless trigonometric ratio value.

5. Frequently Asked Questions (FAQ)

Q1: Why are the results unitless?
A: Trigonometric functions (sine, cosine, tangent) produce ratios of side lengths in right triangles, which are dimensionless quantities.

Q2: Can I use this calculator for angles greater than 360°?
A: Yes, the calculator handles all real angle values as trigonometric functions are periodic.

Q3: What's the difference between the addition and subtraction formulas?
A: The addition formula calculates the function of (A+B), while the subtraction formula calculates the function of (A-B). The sign conventions differ between the formulas.

Q4: Are there restrictions on using the tangent formula?
A: Yes, the tangent formula is undefined when the denominator equals zero (when A±B = 90° + k×180°, where k is an integer).

Q5: Can I use this for hyperbolic trigonometric functions?
A: No, this calculator only handles standard circular trigonometric functions. Hyperbolic functions have different compound angle formulas.