Graphing sin(x) with sliders for amplitude, frequency, and vertical and horizontal changes.
Adjust the amplitude slider in the applet so that it's at 3. What is the distance from the maximum to the minimum on the function g(x). How does that relate to an amplitude of 3?
The distance is 6, it is double the amplitude of 3.
If a Sine function is transformed so it has an amplitude of 6, what will the equation look like?
What does changing the frequency do to the sine function?
It makes it more squished together.
The "period" of a trig function means how many cycles can be found between 0 and 2[math]\pi[/math]. See the photo below:
When you adjust the frequency to 2 on the applet, how many full cycles on the red g(x) function can be seen between 0 and 2[math]\pi[/math]?
Given the graph of the function below, what is the equation of the sine function? (Hint: Use the applet above if needed)
What does changing the vertical slider do to the function?
Slides the graph up or down
If you wanted to take a sine function and slide it down 4 units, what would be the equation of the new function?
If you want to take a function, change its amplitude so that it's 2, adjust the frequency so that it's 4 and slide the function up 2 boxes, what would its equation look like? (Hint: You can use the applet to help!)
Adjust the sliders for amplitude, frequency and vertical shift. How does these changes compare to the changes in the sine function?
What is the equation of the transformed cosine function below? Use the applet to help as needed.
What is the equation of the transformed cosine function below? Use the applet to help as needed.
If you want to take a cosine function, change it so that the distance between the maximum and minimum is 8, so that it has 4 cycles between 0 and 2[math]\pi[/math], and slide the function down 2 boxes, what would its equation look like? (Hint: You can use the applet to help!)