Copy of Period and Frequency Exploration - Sine and Cosine
Hi Kids!!
This exploration will help you to learn a little more about what period and frequency is. Follow the instructions carefully below.
1. look at the x-axis. This axis represents the angle inside the function. With a partner if you like, find the below locations on the x-axis:
a. One Pi
b. One and a half Pi
c. 2Pi
d. 2 and a half Pi
2. Think of the unit circle. After how many radians do you think the sine and cosine functions half completed all the possible values they can produce?
Sine Function
1. Turn off the cosine function by clicking on the dot next to the function. The graph of cosine will disappear
2. The slider changes the values for "B" in the equation f(x)=sin(bx). Set the slider to 1 so you can look at the graph of the standard sine function.
Questions for Your Journal:
1. The period of a trigonometric function is the amount of radians or degrees needed for the function to complete a full cycle and start to repeat itself. when b = 1, after how many radians does the graph of sin(x) start repeating itself?
2. Change the slider to 2, and write the period of the function
3. Change the slider to 0.5 and write the period of the function.
4. Is there a formula you can use to figure out the period without a slider?
Cosine Function
1. Turn off the sine function by clicking on the dot next to the function. The graph of cosine will disappear. Turn on the cosine function.
2. The slider changes the values for "B" in the equation f(x)=cos(bx). Set the slider to 1 so you can look at the graph of the standard sine function.
Questions for Your Journal:
1. The period of a trigonometric function is the amount of radians or degrees needed for the function to complete a full cycle and start to repeat itself. when b = 1, after how many radians does the graph of sin(x) start repeating itself?
2. Change the slider to 3, and write the period of the function
3. Change the slider to 1.5 and write the period of the function.
4. Is there a formula you can use to figure out the period without a slider?
Frequency
Frequency is the amount of full cycles a function completes in 2Pi radians. Can you see a relationship between B and the frequency?