Double Angle Formula Calculator

A double angle simply means an angle that is twice the size of a given angle θ, i.e., 2θ. Double angle formulas are trigonometric identities that express sin(2θ), cos(2θ), and tan(2θ) in terms of sin(θ) and cos(θ). They are widely used to simplify expressions and solve trigonometric equations.

The sine double angle formula is: sin(2θ) = 2·sin(θ)·cos(θ). This means to find the sine of twice an angle, you multiply 2 by the sine of the original angle and the cosine of the original angle.

There are three equivalent forms of the cosine double angle formula: cos(2θ) = cos²θ − sin²θ, cos(2θ) = 1 − 2sin²θ, and cos(2θ) = 2cos²θ − 1. All three are mathematically identical, derived using the Pythagorean identity sin²θ + cos²θ = 1, and you can use whichever form is most convenient for a given problem.

The tangent double angle formula is: tan(2θ) = 2·tan(θ) / (1 − tan²θ). Note that this is undefined when tan²θ = 1, i.e., when θ = 45°, 135°, or equivalent radian values, because division by zero occurs.

No, they are not the same. sin(2x) = 2·sin(x)·cos(x) by the double angle formula, while 2·sin(x) simply doubles the sine value. They are equal only at specific angles, such as x = 0° or x = 90°.

Select your preferred angle unit (degrees or radians), then enter your angle θ. The calculator will automatically apply all the double angle identities and display sin(2θ), all three forms of cos(2θ), and tan(2θ) along with a visual chart of the results.

Use the tangent double angle formula: tan(2θ) = 2·tan(θ) / (1 − tan²θ). With θ = 35°, tan(35°) ≈ 0.7002, so tan(70°) = 2·(0.7002) / (1 − 0.7002²) ≈ 1.4004 / 0.5097 ≈ 2.7475. You can verify this directly with the calculator by entering θ = 35°.

Yes. Select 'Radians' as the angle unit and enter your angle in radians (e.g., π/6 ≈ 0.5236 for 30°). The calculator handles both units and also displays the equivalent radian value of your input for reference.