Double Angle Formula Calculator

Double Angle Formula for Cosine:

\[ \cos(2θ) = \cos²(θ) - \sin²(θ) \]

cos(2θ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Double Angle Formula for Cosine?

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

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

2. How Does the Formula Work?

The formula is expressed as:

\[ \cos(2θ) = \cos²(θ) - \sin²(θ) \]

Where:

\( θ \) — Original angle (in degrees or radians)
\( 2θ \) — Double of the original angle
\( \cos(2θ) \) — Cosine of the doubled angle

Explanation: The cosine of twice any angle can be calculated using just the cosine and sine of the original angle.

3. Importance of the Double Angle Formula

Details: This formula is essential in calculus, physics, and engineering for simplifying trigonometric expressions, solving equations, and analyzing periodic phenomena.

4. Using the Calculator

Tips: Simply enter the angle θ in degrees. The calculator will compute cos(2θ) using the double angle formula.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the range of possible values for cos(2θ)?
A: Like all cosine values, cos(2θ) will always be between -1 and 1.

Q3: Can this formula be used for any angle?
A: Yes, the formula works for all real values of θ, both positive and negative.

Q4: How is this formula derived?
A: It comes from the cosine addition formula: cos(A+B) = cosAcosB - sinAsinB, with A = B = θ.

Q5: What are some practical applications of this formula?
A: It's used in signal processing, electrical engineering, mechanical vibrations analysis, and many physics problems involving periodic motion.