Sin and Cos Graphs

What are the 5 steps to graph the following function? y= -4 sin 2(x+Pi/2)

1. negative sin graph, reflected over the x-axis 2. k=0, axis of wave is the x-axis 3. A= 4, up and down 4 spaces from the axis of wave 4. h= Pi/2 to the left 5. period is Pi. graph starts at -Pi/2 and ends at Pi/2

What are the 5 steps to graph the following function? y= 2 cos (x-Pi/3)

1. sin graph starts at a zero then hits a maximum 2. k=0, axis of wave is the x-axis 3. A=2, up and down 2 spaces from the axis of wave 4. h= Pi/3 to the right 5. period is 2Pi. graph starts at Pi/3 and ends at 7Pi/3

What do A, B, h and k represent in the standard form: y=A sin/cos B (x-h) +k

ABS (A) represents the amplitude B is used to find the period of the graph h is the horizontal shift (starting point of the graph) k represents the axis of wave

Formula for Amplitude

ABS (max-min) / 2

How do you find the values in between the starting and ending point to plot the points of a function?

Add the starting value and the ending value and divide by 2. This will give you the middle value. Then add the starting value and midpoint and divide by 2, and the midpoint and ending value and divide by 2.

Amplitude

Measures the distance from the axis of wave to the maximum or minimum

Formula for Period

Period = 2 Pi /B

Cos

What graph is pictured?

Sin

What graph is pictured?

Tan

What graph is pictured?

Periodic Function

any function that "repeats" after an interval of time

Changing the amplitude of the graph affects the:

height of the graph, maximums and minimums

Axis of Wave

horizontal axis that passes through the center of the function

What does the graph of -sin(x) look like?

it is reflected over the x-axis, it starts at 0 and hits a minimum first

What does the graph of -cos(x) look like?

it is reflected over the x-axis, it starts at a minimum point

What does the graph of cos(-x) look like?

it is the same graph as cos(x)

What does the graph of sin(-x) look like?

same as -sin(x), reflected over the x-axis

A graph with (x+5) as a horizontal shift moves which direction?

to the LEFT of the y-axis 5 units

A graph with (x-3) as a horizontal shift moves which direction?

to the RIGHT of the y-axis 3 units

Changing the period of the graph affects the:

vertical stretch of the graph, starting and ending points