1. What is the Compound Angle Formula for Sine?

Definition: The compound angle formula expresses the sine of the sum of two angles in terms of the sines and cosines of the individual angles.

Purpose: This formula is fundamental in trigonometry and is used to simplify trigonometric expressions and solve equations involving sums of angles.

2. How Does the Formula Work?

The formula is:

Where:

• \( A \) and \( B \) — Angles in degrees
• \( \sin \) — Sine function
• \( \cos \) — Cosine function

Explanation: The sine of a sum of two angles equals the sum of the product of the sine of the first angle and cosine of the second angle, and the product of the cosine of the first angle and sine of the second angle.

3. Importance of Compound Angle Formulae

Details: These formulae are essential in various fields including physics, engineering, and computer graphics where angle combinations frequently occur.

4. Using the Calculator

Tips: Enter any two angles in degrees. The calculator will compute the sine of their sum using the compound angle formula.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used for any angles?
A: Yes, the formula works for all real values of A and B, whether positive or negative.

Q2: Are there similar formulas for other trigonometric functions?
A: Yes, there are compound angle formulas for cosine (cos(A+B)) and tangent (tan(A+B)) as well.

Q3: What's the difference between degrees and radians in this calculation?
A: The calculator converts degrees to radians internally since PHP's trigonometric functions use radians.

Q4: Can I use this for subtraction of angles?
A: Yes, sin(A - B) = sinA cosB - cosA sinB. Just enter a negative value for B.

Q5: Why is the result sometimes greater than 1?
A: The sine function normally ranges between -1 and 1, but floating-point calculations might show values like 1.000000 due to rounding.