Question

I could REALLY use some help, please!!: Generating the graph of the cosine curve.

Answer 1

Please know I truly need help, I'm not just asking for an answer; merely an explanation on what to do! This is the assignment...

Answer 2

1. Using your calculator, make a table including x = 0, ten positive x-values (increments of 30 degrees) and ten negative x-values. Find the corresponding y-values.

2.Plot all 21 of these points.

3.Draw the curve.

4. Answer the following questions:
What is the domain?
What is the range?
What is the y-intercept?
What are the x-intercepts?

5.Also, answer the following questions as you compare the sine and cosine curves.
How are the sine and cosine curves similar?
How are the sine and cosine curves different?

Answer 3

I'd be glad to help. What, specifically, would you like to know about the graph of the cosine function?

Answer 4

I guess really the main points. I'm quite lost on the assignment above.

Answer 5

Are you using a calculator, or a table?
I need for you to pick one or two concepts up front for us to discuss.

Answer 6

Using your calculator, make a table including x = 0, ten positive x-values (increments of 30 degrees) and ten negative x-values.

that means pick some numbers for x

Answer 7

I have a TI-84 plus. I haven't used the graph feature in years. So I could use my calculator.

Answer 8

...but I dunno how.

Answer 9

Are you able to set your calculator to degree mode?

Answer 10

Yes! It's on degree right now.

Answer 11

@kubi-cal: we've got a minor problem here: You've asked both Phi and me to help you. It'd be a waste of effort for the two of us to help you simultaneously. Which of us can you understand more readily? Don't be shy: make your choice.

Answer 12

Well you've come this far, so I'm fine with you helping! c:

Answer 13

Apologies to @phi then, and thanks for handling this matter so graciously.

Answer 14

Yes, thank you!

Answer 15

Sorry about calling you both out for help, just a bit desperate to get this assignment over with honestly.

Answer 16

Good: you have your calculator set to Degree mode. As the problem statement asks, please choose x=0 and ten more values that are multiples of 30 degrees. This means: 0, 30, 60, 90, 120, etc. Comfortable with that?

Answer 17

Sure!

Answer 18

There are certainly faster ways to do this, but (since I don't have my calculator with me), I'm suggesting you calculate the corresponding values of the sine function one by one and write them down. Do this: press the Sin key and then 0, followed by ). Enter. What do you get?

Answer 19

Okay, Sin(0) is 0. Would I then do this with the values? Sin(30), Sin(60), etc?

Answer 20

Please make up a table like this one:

x-value sin x
0 0
30 1/2
60 Sqrt(3)/2

Answer 21

I promise, there are faster ways...we could go into them later, when I have my calculator handy for reference.

Answer 22

While you're typing, I'm going to start a graph for you:

Answer 23

for x=0, makr a black dot at y=0;
for x=30, at y=1/2
for x = 60, at y =Sqrt(3)/ = 0.866

Answer 24

Sorry the site crashed for me!

Answer 25

Okay understood.

Answer 26

Great. So, you mark your x-axis from 0 to 30 in steps of 30 degrees, and then you go in the other direction: -30, -60 , -90, and so on. Is this enuf info for you to continue? or could we move on to the next part of the question?

Answer 27

Lets go ahead and move on!

Answer 28

I don't mean to oversimplify the concept of "domain," but will here in the interest of getting this problem finished. The "domain" is the set of all PERMISSIBLE input (or x-) values. For the sine, the domain includes all real numbers, from -infinity to +infinity. Have you heard or read about "domain" before?

Answer 29

I'm pretty sure I learned about it last semester. But given that I suffer from memory loss, would you mind refreshing my brain?

Answer 30

The "range" is an interval (or intervals) on they-axis. It specifies all values which y may take on.

Answer 31

Regarding domain; certainly we could talk about this more...but as with the calculator, I'd like to address that later.

Answer 32

What appears to be the smallest y value that your sine curve can take on? the largest?

Answer 33

The domain is [smallest y value , largest y value].

Answer 34

Hm. I'm honestly not sure. Sorry.

Answer 35

The RANGE is [smallest y value , largest y value].

Answer 36

Have you tried graphing your sine by connecting the points you've plotted?
What is the y value for x=90 degrees?

Answer 37

OH sorry! I think I understand. That would be 1.

Answer 38

Right, and so your range is simply [-1,1].

Answer 39

Try x- and y-intercept. I must leave this conversation for about 5 minutes, but will be back.

Answer 40

Okay, no worries. The x-int is .5 and there is no y-int, correct?

Answer 41

Let's put the matter this way, in discussing the y-intercept: the y-int. is the POINT at which the graph crosses the y-axis. Can you identify the coordinates of that point?

Answer 42

Oh shoot! -.5!

Answer 43

Well, (o,-.5)