1. What is the Compound Angle Formula?

The compound angle formula for cosine, cos(A+B) = cosA cosB - sinA sinB, is a fundamental trigonometric identity that expresses the cosine 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
• \( \cos \) — Cosine trigonometric function
• \( \sin \) — Sine trigonometric function

Explanation: The formula calculates the cosine of the sum of two angles by combining the products of their individual cosine and sine values.

3. Importance of Compound Angle Formula

Details: This formula is essential in trigonometry, physics, engineering, and signal processing for simplifying expressions involving sums of angles and solving trigonometric equations.

4. Using the Calculator

Tips: Enter angles A and B in degrees. The calculator will compute cos(A+B) using the compound angle formula. The result is unitless as it's a trigonometric ratio.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible values for cos(A+B)?
A: The cosine function ranges from -1 to 1, so cos(A+B) will always be between -1 and 1 inclusive.

Q2: Are there similar formulas for sin(A+B) and tan(A+B)?
A: Yes, sin(A+B) = sinA cosB + cosA sinB and tan(A+B) = (tanA + tanB)/(1 - tanA tanB).

Q3: Can this formula be used for angles greater than 360 degrees?
A: Yes, trigonometric functions are periodic, so the formula works for any real number angles.

Q4: How is this formula derived?
A: The formula can be derived using the unit circle, Euler's formula, or geometric constructions involving right triangles.

Q5: What are some practical applications of this formula?
A: Used in wave interference calculations, rotational transformations, electrical engineering (AC circuits), and mechanical systems analysis.