Mathematics

Permutations & Combinations(PROBABILITY)

Aside from probability, Permutations and Combinations are essential tools for statistics.

Ellipse and its equation

Ellipse is twisted circle, it got major features and equation from circle.

Ellipse got TWO radiuses (or radii):

• Major radius: the longer one.
• Minor radius: the shorter one.

Unit circle

It’s a fairly fundamental tool for solving trigonometric problems.

Reference Angle

The notion reference angle would be the very FIRST thing to understand before solving any trig equations.

First thing first, it’s always the angel with X-axis and Terminal Ray.

Signs of trig functions

Before solving a trig equation, need look at the sign of the equation, AND identify which one or multiple quadrants will the solutions land in.

• Quadrant I: All trig functions are POSITIVE.
• Quadrant II: Only sin(x) is POSITIVE, others…

Complex numbers

Imaginary number

# Assume that
i² = −1
# therefore the imaginary unit is
i = √(-1)

Powers of Imaginary Unit:

The pattern is from i to i⁴, then it repeats.
To evaluate iⁿ, just to get the remainder n % 4 and see…