Calculus: Derivatives and Integrals of Trigonometric Functions

Vocabulary flashcards covering differentiation and integration rules for trigonometric functions and algebraic power functions.

Derivative of $\sin(x)$

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

Derivative of $\cos(x)$

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

Derivative of $\tan(x)$

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

Derivative of $\cot(x)$

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

Derivative of $\sec(x)$

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

Derivative of $\csc(x)$

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

Indefinite Integral of $\cos(x)$

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

Indefinite Integral of $\sin(x)$

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

Indefinite Integral of $\sec^2(x)$

$$\int \sec^2(x)\,dx = \tan(x) + C$$

Indefinite Integral of $\csc^2(x)$

$$\int \csc^2(x)\,dx = -\cot(x) + C$$

Indefinite Integral of $\sec(x)\tan(x)$

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

Indefinite Integral of $\csc(x)\cot(x)$

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