7.4 Graphing Sine (Digital Version)

7.4 Graphing Sine (Digital Version)

By Melodie Hunt

Section 13 - 1: Periodic Relationships

Graphing the relationships of periodic functions.

Periodic Relationships

• A relationship the repeats in the same pattern over the same amount of time.

• Years increase in numbers but repeat the same days.

• The clock repeats itself every hour but it does not stay the same time.

Key Components to ANY Periodic Relation

• Amplitude - identifies the highest and lowest output values.

• Midline - What the amplitude is centered around.

• Period - the interval of time that a relation takes to complete one cycle or rotation. Think a year here...the period would be 365 days.

Finding Amplitude

• Find the highest y - output and the lowest output.

• Calculate the distance between the highest and lowest values.

• Divide it by two...this is the amplitude.

• (2 - (-2)) = 4...4/2 = 2. The amplitude is 2.

Multiple Choice

What is the equation of the graph?

•  y = 2 cos x
• y = sin x
• y = 2 sin x
• y = sin 2x 

Fill in the Blanks

The amplitude of the periodic function is

units.

Fill in the Blanks

The amplitude of the function is

units.

Finding Period

• You can start at one of three places; a highest point, a lowest point, or a zero.

• Find the x - value at that point. Let's start at the coordinate point (-3, 2) this would be a "highest point." The x - value is -3.

• Follow the function until you reach the SAME y - value that you started at. You will use that x - value as the ending point. The point (1, 2) would be the NEXT, same y - value. The x - value is 1.

Finding Period

• The distance between the x - values is the period.

• 1 - (-3) = 4; the period is 4 units.

• You can also simply count!

Fill in the Blanks

The period of this function is

units.

Fill in the Blanks

The period of the function is

units.

Multiple Choice

Which of the following is the amplitude and period of the function?

• Amplitude: 3 units

  Period: 6 units

• Amplitude: -3 units

  Period: 6 units

• Amplitude: 6 units

  Period: 3 units

• Amplitude: -4 units

  Period: 3 units

Multiple Choice

Is the following periodic?

• Yes

• No

Multiple Choice

Is the following function periodic?

• yes

• no

Multiple Choice

The period of a function is

• how long one cycle is before the function repeats

• how high and low the function goes from the center line

• the range of the function

Multiple Choice

What is the period of the function?

• 4

• 2

• 3

• 5

Multiple Choice

The __________ represents half the distance between the max and min of a sine or cosine graph. 

• Period
• Frequency
• Extreme Values
• Amplitude

Multiple Choice

Find the amplitude of the function.

• 3

• 4

• π/4

• 6

Multiple Choice

What is the period of either graph? 
y = sin(x)      &   y = cos (x)

• Pi
• 2Pi
• Pi/2
• Pi/4