notes/education/math/MATH1060 (trig)/Graphing.md

Sine/Cosine

Given the above graph:

• At the origin, sin(x) = 0 and cos(x) = 1
• A full wavelength takes 2\pi

Manipulation

Formula	Movement
y = cos(x) - 1	Vertical shift down by 1
y = 2cos(x)	Vertical stretch by a factor of 2
y = -cos(x)	Flip over x axis
y = cos(2x)	Horizontal shrink by a factor of 2

Periodic Functions

A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a period.

Sinusoidal Functions

A function that has the same shape as a sine or cosine wave is known as a sinusoidal function.

There are 4 general functions:

$$A * sin(B*x - C) + D$$	y = A * cos(B*x -c) + D$$
y = A * sin(B(x - \frac{C}{B})) + D	y = A*cos(B(x - \frac{C}{B})) + D$$

How to find the:

• Amplitude: |A|
• Period: \frac{2\pi}{B}
• Phase shift: \frac{C}{|B|}
• Vertical shift: D

 y = A * \sin(B(x-\frac{C}{B})) 

Tangent/Cotangent