Derivatives and Antiderivatives of Trigonometric and Inverse Trigonometric Functions

These flashcards cover the derivatives and antiderivatives of trigonometric and inverse trigonometric functions, summarizing key formulas and definitions.

What is the derivative of sin(x)?

\frac{d}{dx} \sin(x) = \cos(x)

What is the antiderivative of sin(x)?

\int \sin(x) \,dx = -\cos(x) + C

What is the derivative of cos(x)?

\frac{d}{dx} \cos(x) = -\sin(x)

What is the antiderivative of cos(x)?

\int \cos(x) \,dx = \sin(x) + C

What is the derivative of tan(x)?

\frac{d}{dx} \tan(x) = \sec^2(x)

What is the antiderivative of tan(x)?

\int \tan(x) \,dx = -\ln|\cos(x)| + C

What is the derivative of cot(x)?

\frac{d}{dx} \cot(x) = -\csc^2(x)

What is the antiderivative of cot(x)?

\int \cot(x) \,dx = \ln|\sin(x)| + C

What is the derivative of sec(x)?

\frac{d}{dx} \sec(x) = \sec(x)\tan(x)

What is the antiderivative of sec(x)?

\int \sec(x) \,dx = \ln|\sec(x) + \tan(x)| + C

What is the derivative of csc(x)?

\frac{d}{dx} \csc(x) = -\csc(x)\cot(x)

What is the antiderivative of csc(x)?

\int \csc(x) \,dx = -\ln|\csc(x) + \cot(x)| + C