Six Basic Trig Functions: Key Points

Derivatives of the six basic trig functions

• \frac{d}{dx}\sin x = \cos x
• \frac{d}{dx}\cos x = -\sin x
• \frac{d}{dx}\tan x = \sec^2 x
• \frac{d}{dx}\cot x = -\csc^2 x
• \frac{d}{dx}\sec x = \sec x \tan x
• \frac{d}{dx}\csc x = -\csc x \cot x

Antiderivatives: overview

• You are expected to memorize all six antiderivatives.
• Tangent and cotangent antiderivatives are straightforward; secant and cosecant are more involved.
• Formulas:
• \int \sin x\,dx = -\cos x + C
• \int \cos x\,dx = \sin x + C
• \int \tan x\,dx = -\ln|\cos x| + C = \ln|\sec x| + C
• \int \cot x\,dx = \ln|\sin x| + C
• \int \sec x\,dx = \ln|\sec x + \tan x| + C
• \int \csc x\,dx = -\ln|\csc x + \cot x| + C
• Alternate form for csc: \int \csc x\,dx = \ln|\csc x - \cot x| + C