# Thread: [SOLVED] Different Graphs of Sinx and Cosx

1. ## [SOLVED] Different Graphs of Sinx and Cosx

Hi, I know how to draw simple graphs like sinx, cosx, sin2x, cos2x ... etc.
But I am stuck at the following:

1) 2-2cos3x

2) 3-4cos2x (for 0-180)

3) 2-2cosx+2

Could someone tell me the easiest way to draw these on a graph paper?

I know that 3x or 2x in the above means the # of cycles in a 360 range. But I am confused about what to do when 3-4 or 1-2 is added in-front of the functions like in the above examples.

2. Hello unstopabl3
Originally Posted by unstopabl3
Hi, I know how to draw simple graphs like sinx, cosx, sin2x, cos2x ... etc.
But I am stuck at the following:

1) 2-2cos3x

2) 3-4cos2x (for 0-180)

3) 2-2cosx+2

Could someone tell me the easiest way to draw these on a graph paper?

I know that 3x or 2x in the above means the # of cycles in a 360 range. But I am confused about what to do when 3-4 or 1-2 is added in-front of the functions like in the above examples.
OK. Here's how you do #1.

First, when the graph of $y= \cos3x$ is changed into $y=2\cos3x$, all the $y$-values are multiplied by $2$. In other words, the graph is stretched up and down by a factor of $2$, from the $x$-axis. Instead of taking values from $-1$ to $1$, therefore, it will take values from $-2$ to $+2$.

Next, when $y = 2\cos3x$ is changed into $y = -2\cos3x$, all the $y$-values have their sign changed. In other words, the graph is reflected in the $x$-axis. So, for example, when $x = 0,\; y = -2$ instead of $+2$.

Finally, changing $y = -2\cos3x$ into $y = 2-2\cos3x$ adds $2$ to all the $y$-values. In other words, the graph is shifted (translated) upwards by $2$ units.

So:

• Can you sketch the graph for #1 now?
.
• Can you do #2 in the same way?

***

I assume that for #3 you mean
$y = 2-2\cos(x+2)$
Clearly, this is related to the graph of
$y = 2-2\cos x$
which you can sketch using the same techniques as above. Then, you need to learn that when $x$ is changed into $(x+2)$, the graph is translated $2$ units to the left.

Yes, it is to the left, not the right, because when $x = 0$, the value of $(x+2)$ is $2$. So the new graph starts at the point where $x = 2$ on the original graph. So it is exactly the same as the original, but it's $2$ units to the left. (You may need to think a bit about that!)

Can you complete #3 now?

3. Makes perfect sense! Thanks for the detailed explanation, I have successfully drawn these graphs now

There was a bit confusion in my post regarding #3

The graph to be sketched was (2-2cosx)+2 so how would you draw this one?

Would the +2 at the end just shift the whole graph 2 units upwards on the Y-Axis?

4. Hello unstopabl3
Originally Posted by unstopabl3
Makes perfect sense! Thanks for the detailed explanation, I have successfully drawn these graphs now

There was a bit confusion in my post regarding #3

The graph to be sketched was (2-2cosx)+2 so how would you draw this one?

Would the +2 at the end just shift the whole graph 2 units upwards on the Y-Axis?
I'm not sure what you mean by $(2-2\cos x)+2$. This is just $4 - 2\cos x$, isn't it?