1. What Is The Compound Angle Formula?

The compound angle formula sin(A+B) = sinA cosB + cosA sinB is a fundamental trigonometric identity that expresses the sine of the sum of two angles in terms of the sines and cosines of the individual angles.

2. How Does The Calculator Work?

The calculator uses the compound angle formula:

Where:

• \( A \) — First angle in degrees
• \( B \) — Second angle in degrees
• \( \sin \) — Sine trigonometric function
• \( \cos \) — Cosine trigonometric function

Explanation: The calculator converts angles from degrees to radians, calculates individual trigonometric values, then applies the compound angle formula to compute the result.

3. Applications Of Compound Angles

Details: Compound angle formulas are essential in various fields including physics, engineering, computer graphics, and navigation. They're used to simplify trigonometric expressions, solve wave equations, and analyze periodic phenomena.

4. Using The Calculator

Tips: Enter both angles A and B in degrees (0-360°). The calculator will compute sin(A+B) using the compound angle formula and also show the direct calculation of sin(A+B) for verification.

5. Frequently Asked Questions (FAQ)

Q1: Why use the compound angle formula instead of direct calculation?
A: The formula demonstrates the mathematical relationship and is useful when individual components are known but the sum angle isn't directly available.

Q2: Does this work for angles greater than 360°?
A: Yes, trigonometric functions are periodic, so angles beyond 360° will be reduced to their equivalent within 0-360° range.

Q3: Are there similar formulas for other trigonometric functions?
A: Yes, there are compound angle formulas for cosine (cos(A+B) = cosA cosB - sinA sinB) and tangent (tan(A+B) = (tanA + tanB)/(1 - tanA tanB)).

Q4: Can this be used for angle differences?
A: Yes, sin(A-B) = sinA cosB - cosA sinB follows a similar pattern with a sign change.

Q5: What about triple angle formulas?
A: There are formulas for triple angles too, such as sin(3A) = 3sinA - 4sin³A, which can be derived from compound angle formulas.