[b]Hi Kids!![br][br]This exploration will help you to learn a little more about what period and frequency is. Follow the instructions carefully below.[/b]

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:[br]a. One Pi[br]b. One and a half Pi[br]c. 2Pi[br]d. 2 and a half Pi[br][br]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?[br][br]Sine Function[br]1. Turn off the cosine function by clicking on the dot next to the function. The graph of cosine will disappear[br]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.[br]Questions for Your Journal:[br]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?[br][br]2. Change the slider to 2, and write the period of the function[br][br]3. Change the slider to 0.5 and write the period of the function.[br][br]4. Is there a formula you can use to figure out the period without a slider?[br][br]Cosine Function[br]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.[br]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.[br]Questions for Your Journal:[br]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?[br][br]2. Change the slider to 3, and write the period of the function[br][br]3. Change the slider to 1.5 and write the period of the function.[br][br]4. Is there a formula you can use to figure out the period without a slider?[br][br][br]Frequency[br][br]Frequency is the amount of full cycles a function completes in 2Pi radians. Can you see a relationship between B and the frequency?