## Explore the Trigonometric Functions and Their Graphs
Use the GeoGebra file below to explore how changes in the a, b, c, and d
variables affect their graphs and then answer the questions below. Daniel Couture, October 4, 2009, Created with GeoGebra |

Use the graph above to answer the following questions.

1) How does the a variable affect the graphs qualitatively?2) How does the graph of y = 2 sin(x) differ from the graph of y = sin(x)?

3) How does the b variable affect the graphs qualitatively?

4) How does the graph of y = cos(4x) differ from the graph of y = cos(x)?

5) How does the c variable affect the graphs qualitatively?

6) How does the graph of y = tan(x + 2) differ from the graph of y = tan(x)?

7) How does the d variable affect the graphs qualitatively?

8) How does the graph of y = cos(x) - 4 differ from the graph of y = cos(x)?

9) If provided with the graph of y = 2 sin(3x) + 1, how would you sketch a graph y = 2 csc(3x) + 1?

10) Connect the following vocabulary to the a, b, c, or d variable that controls it.

(period, phase shift, amplitude, vertical shift)

11) How long are the periods for the following functions? (Express your answer in both radians and degrees)

y = sin(x)

y = cos(x)

y = tan(x)

12) If given the equation 3 sin(2x) - 1 = 4, how can you use the graph to conclude that there is no solution?