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A doctor constructed a timeline of the last 18 months. They mapped regions based on the intensity of a patient’s symptoms and found that there was a cyclical pattern. When graphed as a function of intensity, it turned out to be similar to f(x)=sinx
The following information was used for the graph:
• On a scale of 0-10, intensity is ranked, where 0 represents normal and 10 full blown symptom.
•The period is 6 months
•Patient stated that he recalled full blown symptoms first which occurred during month 3.
•Sketch a graph of the functionh(x)  by hand, interval 0≤x≤18

Hi chibi (https://biology-forums.com/index.php?action=profile;u=974927), just be aware that there are an infinite number of possible answers here. I've shown my work for clarity.

(https://biology-forums.com/gallery/42/6_23_01_21_9_23_49.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=42430)

(https://biology-forums.com/gallery/42/6_23_01_21_9_23_55.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=42431)

(https://biology-forums.com/gallery/42/6_23_01_21_9_24_03.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=42432)

Here are some videos to help you out:

https://www.youtube.com/watch?v=pRfQRQeEHsE

https://www.youtube.com/watch?v=-LQ2153aOiY

Let me know if you have any follow up questions :)

Hi @bio_man thanks for the solution. I also watched the 2 videos, which helped me along the way. But just a couple of things, I was given 3 other questions based on the cyclical pattern of the graph. First question states, when did the patient’s first rank his intensity at 7.5? would 0 months be the time where the patient’s first ranked his intensity at 7.5? I plugged in 7.5 into the original equation. (Mainly had difficulty with last 2) Second question, when did the patient’s rank his intensity at 7.5 for the third time? And Third, how high did the patient’s rank the intensity at 12 months?

This is a tricky one because remember our scale is between -5 and 5.

-5 = 0/10
-4 = 1/10
-3 = 2/10
-2 = 3/10
-1 = 4/10
0 = 5/10
1 = 6/10
2 = 7/10
3 = 8/10
4 = 9/10
5 = 10/10

What you could do is set the equation equal to 2.5, because 2.5 corresponds to 7.5/10. Then solve for x.

2.5 = 5sin[(π/3)x–(π/2)]

2.5/5 = sin[(π/3)x–(π/2)]

sin-1(2.5/5) = (π/3)x–(π/2)   ...   make sure your calculator is in radians

π/6 = (π/3)x–(π/2)

π/6 + π/2 = (π/3)x

2π/3 / π/3 = 2 = x

Therefore, the first time this happens is on the 2nd month. You may have also done this through visual inspection by look at the graph.

Okay, so I’m not sure if I’m right about this, but since you have already found the first rank for its intensity at 7.5, on the graph says (2, 2.5), the second question wouldn’t you have to X it 3 times since you already had found the first?

I forgot to mention that if you want 0 to presents 0, and 10 to represent 10, just add + 5 to equation:

y = 5sin[(π/3)x–(π/2)] + 5

It's up to you, or keep the original.


Sorry, I didn't read this.

Yeah, so since it's cyclical, it's going to happen again every 6 months (your period). So add 6 to 2, therefore on month 8 it'll happen again. Then again on month 14 -- that's the third time.


Did you figure this one out? What did you get?

No, I did try though. But it didn’t make sense much as I was looking at the graph. It was mainly the second and third question I had trouble with.

So, is it making sense now?

Yeah, it’s just the third question I’m trying to figure out.

For this, remember chibi (https://biology-forums.com/index.php?action=profile;u=974927) that the x-variable represents months, while the y variable represents intensity. Hence, all you do is sub. in 12 in for x

y = 5sin[(π/3)x–(π/2)]

y = 5sin[(π/3)(12)–(π/2)]

y = -5

Remember the legend:

-5 = 0/10
-4 = 1/10
-3 = 2/10
-2 = 3/10
-1 = 4/10
0 = 5/10
1 = 6/10
2 = 7/10
3 = 8/10
4 = 9/10
5 = 10/10

So @ 12 months, the person records no pain, 0/10 rank.

Hi and Thank you @bio_man, I will remember this for next time.