How to Use the Double Angle Calculator

Enter an angle. The calculator shows sin, cos, and tan of that angle, then sin, cos, and tan of double the angle using the double angle identities.

sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = cos²(θ) − sin²(θ)
tan(2θ) = 2 tan(θ) ÷ (1 − tan²(θ))

These identities fall straight out of the angle-addition formulas by setting both angles equal to θ — sin(A+B) becomes sin(θ+θ), and the cross terms collapse into the doubled versions above. cos(2θ) also has two other equivalent forms, 1 − 2sin²(θ) and 2cos²(θ) − 1, which is why textbooks sometimes show three "different" double angle formulas for cosine when they're really the same identity rearranged with the Pythagorean identity.