Double Angle Calculator

This double angle calculator works out sin(2x), cos(2x) and tan(2x) for any angle x, using the standard double angle identities, so you can check homework, verify a derivation, or evaluate an expression without doing the trigonometry by hand. You enter a single angle and choose whether it is in degrees or radians, and the calculator instantly returns the doubled-angle result: the main sin(2x) figure is shown large, with cos(2x) and tan(2x) alongside it, each rounded for easy reading. Behind the scenes it converts your angle to radians if needed, doubles it, and applies sin(2x) = 2 sin x cos x, cos(2x) = cos squared x minus sin squared x, and tan(2x) = 2 tan x over one minus tan squared x, flagging tan(2x) as undefined at the angles where cos(2x) is zero. These identities fall straight out of the addition formulas when both angles are equal, and they turn up constantly in calculus, integration, physics and engineering, for example when combining waves or simplifying an integral before solving it. The cosine double angle has three equivalent forms, which is useful when you need the answer written in terms of sine only or cosine only. Enter your own angle, or use the worked example for 30 degrees below to confirm the calculator matches your own working before relying on it for a harder problem.

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