Question

What function accurately represents the sine curve for red light?

f(x) = sin pi over 640x

f(x) = sin 640πx

f(x) = sin 320πx

f(x) = sin pi over 320x

Answer 1

OK, again a little intimidating... let's see if we can make sense of the graph.

Answer 2

Okay :c

Answer 3

It seems to me that y = 0 when x = 0, 320, and 640. Those are the three blue dots I think. Do you agree?

Answer 4

Yes. ;o

Answer 5

Alright, so here's a trick for multiple choice tests. Since we know how the graph should work, if we plug in x = 0, 320, and 640 into the correct answer it should give us a y = 0 each time!

Answer 6

Okay, i see, i see.

Answer 7

So does A make sense? How about x = 320? Does that give y = 0?

Answer 8

i dont know how to solve it, but it doesnt look right.

Answer 9

Just to make sure, what doesn't look right to you?

Answer 10

Actually, no. Isnt it supposed to be in that form? like Pi over something.

Answer 11

Alright... you are on a good track... let's carefully check each one.

Answer 12

First, though, do you have sin(pi/2) memorized?

Answer 13

(0,1)?

Answer 14

Yes, that's right. So which one is sin(pi/2) is that 0 or 1?

Answer 15

1.

Answer 16

Good, that will be helpful in just a moment. :)

Answer 17

Back to A, here's what I see when I plug in x = 320.

Answer 18

sin(pi/640 * 320) = sin(320pi/640) = sin(pi/2) = 1 Does that make sense?

Answer 19

OOO Yeah.

Answer 20

But we know that when x = 320, the graph is SUPPOSED TO BE y = 0, so A is impossible.

Answer 21

Yeah, i knew it didnt look right. :o

Answer 22

Yep, your instinct was correct. But you also thought that the "form" looked right. Let's trust that intuition and look at D next, maybe that is our friend. :)

Answer 23

Hopefully :c

Answer 24

Alright, so we are considering sin(pi/320 * x) What do we get when x = 0? This is probably easy.

Answer 25

0 ;o

Answer 26

So far so good. Let's check when x = 320.

Answer 27

I'm getting sin(pi) is that what you got?

Answer 28

Uhh, Yeah. i did.

Answer 29

OK, what is sin(pi) equal to?

Answer 30

Alright, here's a bonus tip then, when the angle is pi, the coordinate is (-1, 0)

Answer 31

OHH. Ohhkay. i see.

Answer 32

So, is sin(pi) going to be -1 or 0?

Answer 33

0

Answer 34

Alright, I'm hoping this one works that's 2 out of 3 zeros so far! One more to check... x = 640.

Answer 35

What do you see?

Answer 36

oh, my calculator died o-o now i have to find batteries. .___.

Answer 37

Well, you could probably use the computer calculator :)

Answer 38

I Should. xD

Answer 39

What are we plugging 640 in?

Answer 40

D, so sin(pi/320 * x)

Answer 41

2?

Answer 42

well, sin(2pi) is what you mean right?

Answer 43

Yeah.

Answer 44

Cool, so we have to have that memorized or calculate it

Answer 45

sin(2pi) corresponds to the angle 2 pi, which has the coordinate (1, 0)

Answer 46

OH. So D's the answer? ;o

Answer 47

It appears to be the case.

Answer 48

The others also give you y = 0 for x = 0, 320, 640, but they are the wrong form... they will compress the graph since they are multiplying instead of stretching the graph like we want

Answer 49

OH YAY

Answer 50

YAHOO!