1. What is the Cos(2θ) Formula?

The double angle formula for cosine, cos(2θ) = 1 - 2 sin²(θ), is a trigonometric identity that relates the cosine of twice an angle to the sine of the original angle. It's one of several double-angle formulas in trigonometry.

2. How Does the Calculator Work?

The calculator uses the double angle formula:

Where:

• \( \sin(θ) \) — Sine of angle θ (must be between -1 and 1)
• \( θ \) — Angle in degrees or radians

Explanation: The formula provides a way to calculate the cosine of double an angle when you know the sine of the original angle.

3. Importance of Double Angle Formula

Details: Double angle formulas are fundamental in trigonometry and have applications in calculus, physics, and engineering. They're particularly useful for simplifying trigonometric expressions and solving trigonometric equations.

4. Using the Calculator

Tips: Enter the sine value (must be between -1 and 1) and select whether your angle is in degrees or radians. The calculator will compute cos(2θ) using the double angle formula.

5. Frequently Asked Questions (FAQ)

Q1: What range of values can I enter for sin(θ)?
A: The sine function only produces values between -1 and 1, so your input must be in this range.

Q2: Are there other double angle formulas for cosine?
A: Yes, cos(2θ) can also be expressed as cos²(θ) - sin²(θ) or 2cos²(θ) - 1.

Q3: Why would I need to calculate cos(2θ) from sin(θ)?
A: This is useful when you know the sine of an angle but need the cosine of its double, which occurs in many physics and engineering problems.

Q4: Does the angle unit (degrees/radians) affect the result?
A: No, because the calculation uses only the sine value, not the angle directly. The unit selection is for your reference only.

Q5: What if I get a result outside [-1, 1]?
A: This shouldn't happen with valid inputs, as cosine values always fall between -1 and 1. Check that your sin(θ) input is valid.