# Basics

Basic Math Skills

This page contains some important stuff that is assumed as basic math knowledge when taking Calculus.

## Equations #

• $a^2 - b^2 = (a+b)(a-b)$

## Trigonometry #

• Cosecant: $\csc{x} = \frac{1}{\sin{x}}$
• Secant: $\sec{x} = \frac{1}{\cos{x}}$
• Cotangent: $\cot{x} = \frac{1}{\tan{x}} = \frac{\cos{x}}{\sin{x}}$

### Exact values #

$x$$\sin x$$\cos x$$\tan x 0$$0$$1$$0$
$\frac{1}{6}\pi$$\frac{1}{2}$$\frac{1}{2}\sqrt{3}$$\frac{1}{3}\sqrt{3} \frac{1}{4}\pi$$\frac{1}{2}\sqrt{2}$$\frac{1}{2}\sqrt{2}$$1$
$\frac{1}{3}\pi$$\frac{1}{2}\sqrt{3}$$\frac{1}{2}$$\sqrt{3} \frac{1}{2}\pi$$1$$0$-

### Identity rules #

• $\sin^2 x + \cos^2 x = 1$
• $\tan^2 x + 1 = \sec^2 x$ (divided by $\cos^2 x$)
• $1 + \cot^2 x = \csc^2 x$ (divided by $\sin^2 x$)
• $\sin(x + y) = \sin(x)\cos(y) + \cos(x)\sin(y)$
• $\sin(x - y) = \sin(x)\cos(y) - \cos(x)\sin(y)$
• $\cos(x + y) = \cos(x)\cos(y) + \sin(x)\sin(y)$
• $\cos(x - y) = \cos(x)\cos(y) - \sin(x)\sin(y)$
• $\sin(2x) = 2\sin(x)\cos(x)$
• $\cos(2x) = \cos^2(x) - \sin^2(x) = 2 \cos^2(x) - 1 = 1 - 2 \sin^2(x)$

## Symetric functions #

• Even functions: $f(-x) = f(x)$
• Odd functions: $f(-x) = -f(x)$