Double Angle Identity Calculator

Double Angle Identities:

\[ \cos(2θ) = \cos²θ - \sin²θ \] \[ \sin(2θ) = 2\sinθ\cosθ \] \[ \tan(2θ) = \frac{2\tanθ}{1 - \tan²θ} \]

Result:

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1. What Are Double Angle Identities?

Double angle identities are trigonometric formulas that express trigonometric functions of double angles (2θ) in terms of single angles (θ). They are useful for simplifying trigonometric expressions and solving equations.

2. How Does the Calculator Work?

The calculator uses the following double angle identities:

\[ \cos(2θ) = \cos²θ - \sin²θ \] \[ \sin(2θ) = 2\sinθ\cosθ \] \[ \tan(2θ) = \frac{2\tanθ}{1 - \tan²θ} \]

Explanation: The calculator first converts your angle from degrees to radians, then applies the appropriate double angle formula based on your selection.

3. Importance of Double Angle Formulas

Details: These identities are essential in calculus, physics, and engineering for simplifying integrals, solving wave equations, and analyzing periodic phenomena.

4. Using the Calculator

Tips: Enter any angle in degrees, select the trigonometric function you want to calculate for the double angle. The calculator will show both the result and the formula used.

5. Frequently Asked Questions (FAQ)

Q1: Can I use radians instead of degrees?
A: This calculator currently accepts degrees only. Convert radians to degrees first (1 radian ≈ 57.2958°).

Q2: Why are there multiple forms of cos(2θ)?
A: The cosine double angle has three forms: cos²θ - sin²θ, 2cos²θ - 1, and 1 - 2sin²θ. All are equivalent through the Pythagorean identity.

Q3: What about other multiple angle formulas?
A: There are also triple angle and half-angle identities, but this calculator focuses on double angles.

Q4: How accurate are the results?
A: Results are accurate to 6 decimal places, using PHP's built-in trigonometric functions.

Q5: Can I calculate inverse trigonometric functions?
A: This calculator only calculates standard trigonometric functions of double angles.