Double Angle Calculator

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This calculator can easily compute trigonometric functions involving double angles (2θ), including sine, cosine, and tangent.

You can input an angle, select the unit (degrees or radians), and choose the desired function (sin(2θ), cos(2θ), or tan(2θ)).

You can see step-by-step explanations. It also displays the formula and detailed calculations.

This makes it a useful tool for learning how to solve double-angle trigonometric problems by hand.

How to Calculate Double Angle?

To calculate the double angle of a trigonometric function like sine, cosine, or tangent, use these simple calculations for each:

Double Angle Formula for Sine:

The formula for the sine of a double angle is:

sin⁡(2θ) = 2⋅sin⁡(θ)⋅cos⁡(θ)

Example:

Let’s calculate 45

sin⁡(2θ) = 2⋅sin⁡(θ)⋅cos⁡(θ)

sin⁡(2×45∘) =

First, find sin⁡(45∘) and cos⁡(45∘):

sin⁡(45∘ )= √2/2 ≈ 0.7071

cos⁡(45∘) = √2/2 ≈ 0.7071

Apply the formula:

sin⁡(2×45∘) = 2⋅0.7071⋅0.7071 = 2⋅ 0.5 = 1

Thus, sin⁡(90∘) = 1.

Double Angle Formula for Cosine:

There are three variations of the cosine double-angle formula:

cos⁡(2θ) = cos⁡2(θ) − sin⁡2(θ)

or

cos⁡(2θ) = 2⋅ cos⁡2(θ) −1

or

cos⁡(2θ) = 1 − 2⋅sin⁡2(θ)

Double Angle Formula for Tangent:

The formula for the tangent of a double angle is:

tan⁡(2θ) = 2tan⁡(θ) / 1−tan⁡^2(θ)

Example:

Angle 30°:

Let’s calculate tan⁡(2×30∘).

tan⁡(30°) = 1/√3 ≈ 0.5774

Apply the formula:

tan⁡(2×30°) = 2 * 0.57741 − (0.5774) /1−(0.5774)^2

= 2 * 0.5774​/1−0.33332 = 1548/0.66671. ​≈ 1.732

Thus, tan⁡(60∘) ≈ 1.732

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