Week 5 Graphs of Sine and Cosine Functions

Week 5

Domain: All Real Numbers.

Range: [1; 1]

Period: P = 2

Quarter Period: 2 =4 = =2.

The Fundamental Cycle: [0; 2 ]

Symmetry: The graph of y = cos x is symmetric about the y-axis. The

function y = cos x is an even function. That is, cos(x) = cos x.

Changes in Amplitude

Multiplying a function by a positive number a will stretch the graph verti-

cally if a > 1 and compress the graph vertically if 0 < a < 1.

Domain: All Real Numbers.

Range: [1; 1]

Period: P = 2

Quarter Period: 2 =4 = =2.

The Fundamental Cycle: [0; 2 ]

Symmetry: The graph of y = sin x is symmetric about the origin. The

function y = sin x is an odd function. That is, sin(x) =  sin x

Learned from Khan Academy  

(I missed a few days of Math had to get caught up)

Find the Amplitude.... 

What is the Amplitude...?

The Amplitude of y= a sin x and y= a cos x represents half the distance between the maximum and minimum values of the function and is given by 

Amplitude=Absolute Value of "a"

Then find the period....

What is the period...?

The period is 2p(pie)/b equations y=a sin bx and y= a cos bx is given by Period 2p/b

Khan Academy helped me tremendously I didn't know how to do anything. It has now caught me up with my class. #Psyched