cycles and periods of sine curves - 3/13/13

Topic: Periodic Functions

Aim: How can we find the period of a sine curve?

•Do Now:

•If Θ = π, find y, if y = sin Θ

•The sine curve

 Find the sin π

•Y = sin 4x

•Finding the period of the sine curve

•Use the graph of y = sin 4x to find:

•A) how many cycles occur in the graph?

–The graph shows 4 cycles

–

B) The period of the function:

  divide the interval of the graph by the number of cycles

2π /4 = π/2; therefore the period of y = sin 4x is π/2

•Got it? Page 844 #2 a,b

•How many cycles occur in the graph?

•What is the period of the sine curve for each?

•Exit slip

•How do you find the number of cycles in the sine curve?

–Identify the smallest repeating section of the graph and count the number of times it occurs.

–For the graph below, find the number of cycles

•The sine function

•Y = sin Θ

•Where Θ (angle in standard position) is matched with the y coordinate of a point on the unit circle.

•This point is where the terminal side of the angle intersects the unit circle.

•You can graph the sine function in radians or degrees (the x values or inputs)