1. What is the Double Angle Formula for Sine?

The double angle formula for sine states that the sine of twice an angle is equal to twice the sine of the original angle multiplied by the cosine of the original angle. This trigonometric identity is useful for simplifying expressions and solving equations.

2. How Does the Calculator Work?

The calculator uses the double angle formula:

Where:

• \( θ \) — Angle in degrees
• The formula works for any angle θ

Explanation: The calculator converts the input angle from degrees to radians, then applies the trigonometric functions to compute the result.

3. Importance of Double Angle Formulas

Details: Double angle formulas are fundamental in trigonometry and have applications in physics, engineering, and signal processing. They help simplify complex trigonometric expressions and solve equations.

4. Using the Calculator

Tips: Enter the angle θ in degrees. The calculator will compute sin(2θ) using the double angle formula. The result is unitless as it's a trigonometric ratio.

5. Frequently Asked Questions (FAQ)

Q1: Does the angle need to be in degrees or radians?
A: The calculator accepts angle input in degrees and converts it internally to radians for calculation.

Q2: What is the range of possible values for sin(2θ)?
A: Like all sine functions, the output ranges between -1 and 1 inclusive.

Q3: Can I use this for negative angles?
A: Yes, the formula works for all real numbers, including negative angles.

Q4: How accurate is the calculation?
A: The calculator uses PHP's built-in trigonometric functions which are highly accurate.

Q5: Are there other double angle formulas?
A: Yes, there are double angle formulas for cosine and tangent as well.