Solving 2sin(2x): Table of Values & Graph

In summary, the function f(x)=2sin(2x) has a compressed horizontal wave and stretched vertical amplitude, but the sine will still repeat from negative infinity to infinity. Therefore, a table of values can still be made for the domain (-pi,pi). To make a table, one can start with a table of values for sin(x), and then create a new table with half the starting point and double the amplitude. This will plot the points for (-pi/2,pi/2) and then use the same y values for (-pi,-pi/2) and (pi/2,pi).
  • #1
DethRose
101
0
I have a question that says: prepare a table of values and plot the graph for the domain (-pie,pie) for the function f(x)=2sin(2x)

I understand how to do that for y=sinx, but for this function the wave compresses horizontally and stretches vertically so isn't the domain now (-pie/2,pie/2) and then therefore how can you make a table of values for (-pie,pie).

thanks for any help
andrew
 
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  • #2
Are you sure you aren't confusing domain and range? It's true that the wave is now compressed horizontally, but the sine will still stretch from negative infinity to infinity. On the interval (-pi,pi), the graph will repeat itself, but there is a graph there, so you can definitely make a table of values for it. If you don't see what I mean, try graphing your function. There will be y-values for the interval (-pi,pi).
 
  • #3
The interval that you are implying is the period of the sine wave. When it is changed to 2*sin(2x), you receive double the amplitude, but half of the period, so if your domain is reflective of the period, then cutting it in half would be valid. The period represents the repeating of the sine wave.

To make a table of it I would first make a table of just plain sin(x). What you would then do is make a new table and start at half of the starting point of the first table and write your y values at intervals of half of the previous table until the maximum value of x at half of the first table. The table should then be the same size. You then double the y values and put them into the table because of the doubled amplitude. This plots (-pi/2,pi/2). Then for the plot of (-pi,-pi/2), you use the same y values as (0,pi/2), and for (pi/2,pi), you use the same y values as (-pi/2,0).

I hope I answered your question.

Da Jeans
 

1. What is the equation for solving 2sin(2x)?

The equation for solving 2sin(2x) is y = 2sin(2x). It is a trigonometric function that involves the sine of 2 times the variable x.

2. How do I create a table of values for 2sin(2x)?

To create a table of values for 2sin(2x), you first need to choose values for the variable x. Then, plug those values into the equation y = 2sin(2x) and solve for y. Repeat this process for different values of x to create a table of corresponding values for y.

3. What do the values in the table represent for 2sin(2x)?

The values in the table represent the output or the y-values for the equation y = 2sin(2x). They show the relationship between the variable x and the resulting value of y.

4. How do I graph 2sin(2x)?

To graph 2sin(2x), first choose values of x and solve for y to create a table of values. Then, plot these points on a coordinate plane and connect them to create a smooth curve. The resulting graph will be a sinusoidal wave.

5. What is the period and amplitude of 2sin(2x)?

The period of 2sin(2x) is π, which means that the graph will repeat itself every π units. The amplitude is 2, which represents the maximum vertical distance between the highest and lowest points on the graph.

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