List of basic formulas in mathmatics

, here are some basic formulas across different branches of mathematics:

### Algebra:
1. Quadratic Formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
2. Distance Formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
3. Slope of a Line: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

### Geometry:
1. Area of a Rectangle: \(A = \text{length} \times \text{width}\)
2. Area of a Circle: \(A = \pi r^2\)
3. Pythagorean Theorem: \(a^2 + b^2 = c^2\) (for right triangles)

### Trigonometry:
1. Sine: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)
2. Cosine: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
3. Tangent: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)

### Calculus:
1. Derivative of a Function: \(f'(x) = \lim_ \frac{f(x + h) - f(x)}{h}\)
2. Integral of a Function: \(\int f(x) \,dx\)

### Probability and Statistics:
1. Mean/Average: \(\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\)
2. Standard Deviation: \(\sigma = \sqrt{\frac{\sum{(x_i - \mu)^2}}{N}}\)
3. Probability: \(P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)
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