Question by Indy: How to graph cycles of cosine and sine functions…?
So for my final exam I have to know how to “graph one cycle of a cosine or sine function, without using a graphing calculator. and show all my work”… I don’t even know how to solve a problem like that for example: y=3sin(1/3x+ pi/2)-2 or y=2cos(1/2x+pi/3)-1… Can someone tell me the steps or ways I could do this? any helpful tips or references would be great!
Thanks!
Best answer:
Answer by ^Pikachu^
You know, on my last test, I had the same problem as you, but once you get the hang of it, sine and cosine graphs are really easy to graph:
*Note that what I’m about to do here is basically the same for both sine and cosine graphs 
Okay. Start with the simple stuff. Finding the period and amplitude of the function.
Let’s do the problem: y = 3 sin (1/3 x + π/2)
The amplitude is the simplest one of all. It’s basically just the number in front of the sine or cosine. In this case, the amplitude would be 3. It’s purpose is to determine how high and how low your graph goes. So on your y-axis, it should go from -3 to 3. Nothing higher, nothing lower.
As for your period, it’s 2π / b. “b” is always the number in front of the x. In this case, it’s 1/3. So the period would be 2π / 1/3, which is equal to 6π. This means that every 6π, your graph repeats. So depending on how you do it, you could start labeling your graph right now!
On the x, go from 0 and increment on the x-axis by either π or 2π, your choice, depending on how many cycles you need to graph. After you know the amplitude and period, start plugging and chugging! >:O
I suggest getting the TI-30XS, which is what I use since it gives you the exact value, such as sin π/3 = √3 / 2.
Most of your points on the graph will be simple ones.
So the last step after plugging in all the points into the equation (π, 2π, 3π, etc..) would be to connect the dots and make the curve and BAM! You now have your very own sine and/or cosine graph 
Well, if you have any questions, go ahead and email me or leave me a message 
What do you think? Answer below!
