derivatives and integrals of trig 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 csc(x)

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

Derivative of sec(x)

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

Derivative of cot(x)

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

Integral of sin(x)

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

Integral of cos(x)

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

Integral of sec^2(x)

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

Integral of csc²

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