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: $f(-x) = -f(x)$