Double Angle Formula Calculator

Enter an angle θ (in degrees or radians) and the Double Angle Formula Calculator computes all three double angle identities at once — sin(2θ), cos(2θ) (all three forms), and tan(2θ). Choose your preferred unit, type in your angle, and get the exact trigonometric values using the standard double angle identities. Also try the calculate Inverse Trigonometric Functions Result (Principal Value).

Results

sin(2θ)

cos(2θ) = cos²θ − sin²θ

cos(2θ) = 1 − 2sin²θ

cos(2θ) = 2cos²θ − 1

tan(2θ)

θ in Radians

2θ (Double Angle)

What is a double angle in trigonometry?

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. See also our calculate sin(A), cos(A) & tan(A) — Trig Identities.

What is the sine double angle formula?

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.

How many forms does the cosine double angle formula have?

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.

What is the tangent double angle formula?

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. You might also find our Sine Calculator (sin) useful.

Is 2sin(x) the same as sin(2x)?

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°.

How do I use this double angle formula calculator?

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.

How do I calculate tan(70°) given tan(35°)?

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°.

Can I use radians instead of degrees with this calculator?

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.