Graphs of Sine & Cosine Functions

Author:L. Marizza A. Bailey, Tim Brzezinski

Topic:Cosine, Functions, Function Graph, Sine, Geometric Transformations, Trigonometric Functions

Move the knob on each slider and observe what each does. Make sure to take note so that you can answer the questions in the subsequent tasks.

1.

The parameter a is called the amplitude of either graph. How would you describe the term amplitude in your own words?

2.

What does the amplitude a do to the graph of either function?

Select all that apply

A
As increases, the graph of sine and cosine stretch vertically
B
As increases, the graph of sine and cosine stretch horizontally
C
As increases, the graph of sine and cosine shift vertically
D
As increases, the graph of sine and cosine shift horizontally

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3.

The period of a function is the length of the largest interval in its domain before it repeats itself.The sine and cosine functions are said to be periodic functions because they have periods. To learn more about periodic functions, click here. What is the period of both parent functions or ? (If you need a hint, click here.)

Select all that apply

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4.

The parameter b gives the period of the function by the formula . What happens to the wave if b is between 0 and 1?

Select all that apply

A
The graph of the function stretches horizontally.
B
The graph of the function stretches vertically.
C
The graph of the function contracts horizontally.
D
The graph of the function contracts vertically.

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5.

How does the parameter c affect the graph of either parent function? How does the graph of this parent function change as c increases

Select all that apply

A
The graph of the parent function shifts horizontally to the right
B
The graph of the parent function shifts horizontally to the left
C
The graph of the parent function shifts vertically up
D
The graph of the parent function shifts vertically down

Check my answer (3)

6.

How does the parameter d affect the graph of either parent function? How does the graph of this parent function change as d increases?

Select all that apply

A
The graph of the parent function shifts horizontally to the right
B
The graph of the parent function shifts horizontally to the left
C
The graph of the parent function shifts vertically up
D
The graph of the parent function shifts vertically down

Check my answer (3)

Graphs of Sine & Cosine Functions

1.

2.

3.

4.

5.

6.

7. Move the sliders to create a sine graph with amplitude: 3 and period 2 (or close to it)

8. Move the sliders to create a cosine graph with amplitude: 2 and period 3 (or close to it) shifted down by 1.

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