What you need to know:
One period is the length of one cycle in degrees or radians, the formula for period is 2pi / |b|
The amplitude is the highest or lowest point from the middle axis also known as |a|, the formula for amplitude is max-min / 2
Basic Sine Function
Basic Cosine Function
Now you know everything you need to know to graph a Sine or Cosine function, let's get started!
Example 1: graph the function y = cos ( x + 45) -2
This means that the function must move 45 degrees ( or pi/2 ) to the left and 2 units down
period: 2pi / |b| = 2pi / 1 = 2pi
amplitude = 1
phase shift: move pi / 2 to the left
Vertical Displacement: 2 units down
Example 2: y= sin (x + pi/2) + 1
The function must go pi/2 ( or 90 degrees) to the left and 1 unit up
period : 2pi / |b| = 2pi / 1= 2pi
amplitude: 1
phase shift : pi/2 to the left
vertical displacement : 1 units up
And WALLAH that's how you graph transformed sine and cosine functions! Hope this was helpful and simple enough for all of you to understand ! (:
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