Im stuck Question a bout graphing sin and plotting points

In summary, the conversation is about graphing y = -4 sin x. The interval is divided into four sub intervals of equal length, each of length pi/2. The points are plotted at the midpoints of each interval, with the x-values being pi/2, pi, 3pi/2, and 2pi. The y-values are determined by evaluating sin at each of these points. The same process is repeated for another interval, [pi/2, 13pi/2], where the midpoint is marked at 7pi/2. The starting point and midpoint are averaged to get the other two intervals.
  • #1
nukeman
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0

Homework Statement



Im doing a question where I have to graphc y = -4 sin x

Ok well I got the period and amplitude, so I have the interval of [0, 2pi]

Now, in order to plot points, I have to divide the interval into 4 sub intervals.

I don't understand how I do that! This is where I get stuck, and don't know how to plot the points now.

Any help would be great!

Homework Equations





The Attempt at a Solution



In my book it says " We divide the interval [0, 2pi] into 4 sub intervals, each of length 2pi/4 = pi/2

I don't get that.
 
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  • #2
Do just what it says, divide the interval [0,2[itex]\pi[/itex] ] into 4 intervals. They even tell you what points to use. Now just evaluate sin at each of those points, this will tell how to draw the graph.
 
  • #3
Integral said:
Do just what it says, divide the interval [0,2[itex]\pi[/itex] ] into 4 intervals. They even tell you what points to use. Now just evaluate sin at each of those points, this will tell how to draw the graph.

I am not confident on how to divide the intervals.

I know for this one I can just refer to the unit circle, and get,

pi/2, pi, 3pi/2, 2pi

And those are my x cords right? and my y cords would just be -4, 0, 4 0

But given the fact that I am not 100% confident in dividing the intervals, how would I divide the following interval into 4 sub intervals?

[pi/2, 13pi/2]
 
  • #4
When they say divide into four intervals, they mean four equal intervals. Mark 0 and [itex]2\pi[/itex] on our x-axis, then mark the midpoint- which divide the interval from 0 to [itex]2\pi[/itex] into two intervals, then mark the midpoint of each of those to get four intervals.

Look at a graph of sin(x) itself. It starts at (0, 0), goes up to [itex](\pi/2, 1)[/itex], down to [itex](\pi, 0)[/itex], continues down to [itex](3\pi/2, -1)[/itex], then goes back up to [itex](2\pi, 0)[/itex]- and then repeats.

So when you have decided where you want 0 to [itex]2\pi[/itex] line, mark first the midpoint. That will be, of course, at [itex](2\pi)/2= \pi[/itex]. That divides the line into two intervals, from 0 to [itex]\pi[/itex] and from [itex]\pi[/itex] to [itex]2\pi[/itex]. Now mark the midpoint of each those intervals, at [itex]\pi/2[/itex] and [itex]3\pi/2[/itex]. At those last two points, mark 4 units below and 4 units above the axis.

Your graph will start at (0, 0), go down to [itex](\pi/2, -4)[/itex] at that first "quarter point" you marked,up to the axis at the middle point, [itex](\pi, 0)[/itex], up to [itex](3\pi/2, 4)[/itex] and finally back down to [itex](2\pi, 0)[/itex]

For [itex]\pi/2[/itex] to [itex]13\pi/2[/itex], the midpoint will be the average of the two numbers: [itex](\pi/2+ 13\pi/2)/2= 14\pi/4= 7\pi/2[/itex] so mark that point. Now average [itex]\pi/2[/itex] and [itex]7\pi/2[/itex], [itex](\pi/2+ 7\pi/2)/2= 8\pi/4= 2\pi[/itex], and average [itex]7\pi/2[/itex] and [itex]13\pi/2[/itex], [itex](7\pi/2+ 13\pi/2)/2= 20\pi/4= 5\pi[/itex].

BUT when you are drawing the graphs, what you really want to do is "eyeball" those points. It should be pretty easy to mark the midpoint of an interval without calculating anything.
 
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  • #5
HallsofIVY - Great, thanks! But I have a question.

in regards to: For π/2 to 13π/2, the midpoint will be the average of the two numbers: (π/2+13π/2)/2=14π/4=7π/2 so mark that point. Now average π/2 and 7π/2, (π/2+7π/2)/2=8π/4=2π, and average 7π/2 and 13π/2, (7π/2+13π/2)/2=20π/4=5π.

As you stated, the midpoint wuold be 7pi/2 - How and where do I know to put that point??
 
  • #6
How do you know where to put "0" and "[itex]13\pi/2[/itex]"? In order to graph anything, you have to have a coordinate system which means you must have and x-axis, marked with x-values.

Are you simply saying that you don't know what number [itex]7\pi/2[/itex]?

[itex]\pi= 3.1715926...[/itex] so [itex]7\pi= 21.991148575128552669238503682957[/itex] and [itex]7\pi/2=10.995574287564276334619251841478[/itex]

(Using the Windows calculator.)
 
  • #7
You can still use a calculator can't you?
 
  • #8
HallsofIvy said:
How do you know where to put "0" and "[itex]13\pi/2[/itex]"? In order to graph anything, you have to have a coordinate system which means you must have and x-axis, marked with x-values.

Are you simply saying that you don't know what number [itex]7\pi/2[/itex]?

[itex]\pi= 3.1715926...[/itex] so [itex]7\pi= 21.991148575128552669238503682957[/itex] and [itex]7\pi/2=10.995574287564276334619251841478[/itex]

(Using the Windows calculator.)


I would just put 7pi/2 half way between the 2 intervals. And to get the other 2 intervals I just average the starting point and midpoint, and the midpoint and the end interval?
 

FAQ: Im stuck Question a bout graphing sin and plotting points

What is the difference between graphing sin and plotting points?

Graphing sin involves plotting the values of the sine function on a coordinate plane, while plotting points refers to marking specific points on a graph.

How do I graph sin on a coordinate plane?

To graph sin, you can use a calculator to find the values of the sine function for different input values and plot these points on a coordinate plane. Alternatively, you can use the unit circle to find the values of sin for specific angles and plot those points.

What is the purpose of graphing sin?

Graphing sin can help us visualize the behavior of the sine function and understand its properties, such as its periodicity and amplitude. It can also be used to solve equations involving the sine function.

How do I plot points for a sine function?

To plot points for a sine function, you can choose different input values, calculate the corresponding output values using a calculator or the unit circle, and then plot these points on a coordinate plane. The more points you plot, the more accurate your graph will be.

What are some common mistakes when graphing sin and plotting points?

Some common mistakes when graphing sin and plotting points include incorrectly labeling the axes, plotting points in the wrong quadrant, and using incorrect values for the sine function. It is important to double check your work and use a graphing calculator or reference guide to ensure accuracy.

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