1. What is the Cos Double Angle Formula?

Definition: The double angle formula for cosine relates the cosine of twice an angle to the cosine of the original angle.

Purpose: It's used to simplify trigonometric expressions and solve trigonometric equations involving double angles.

2. How Does the Formula Work?

The formula is expressed as:

Where:

• \( θ \) — Original angle (degrees or radians)
• \( \cos(θ) \) — Cosine of the original angle
• \( \cos(2θ) \) — Cosine of the double angle

Explanation: The formula allows you to calculate the cosine of twice an angle using only the cosine of the original angle.

3. Importance of the Double Angle Formula

Details: This identity is fundamental in trigonometry, calculus, and physics. It's used in wave equations, harmonic motion analysis, and simplifying complex trigonometric expressions.

4. Using the Calculator

Tips: Enter any angle in degrees (0-360 or beyond). The calculator will compute both cos(θ) and cos(2θ) using the double angle formula.

5. Frequently Asked Questions (FAQ)

Q1: Are there other forms of the cos double angle formula?
A: Yes, it can also be expressed as cos(2θ) = 1 - 2sin²(θ) or cos(2θ) = cos²(θ) - sin²(θ).

Q2: Does this work for any angle measure?
A: Yes, the formula works for all real numbers, whether in degrees or radians.

Q3: How is this formula derived?
A: It comes from the cosine addition formula: cos(A+B) = cosAcosB - sinAsinB when A=B=θ.

Q4: What's the range of possible outputs?
A: Both cos(θ) and cos(2θ) will always be between -1 and 1, inclusive.

Q5: Can this be used for half angles?
A: Yes, by solving for cos(θ) in terms of cos(θ/2), you can derive half-angle formulas.