Sinusoidal Functions: describe transformations, sketch graph

  • #1

Homework Statement


upload_2016-8-13_1-38-49.png


Homework Equations


none

The Attempt at a Solution



-amplitude is 3
-period is 180°
-right 60°
-down 1

Rough sketch of graph:

upload_2016-8-13_1-42-40.png



I would like to know if the graph looks right, is there any improvements to be made?

Thanks :)
 

Answers and Replies

  • #2
blue_leaf77
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You got it wrong. That's the graph of ##y = -3\sin(2(x-60^o))-1##.
 
  • #5
You got it wrong. That's the graph of y=−3sin(2(x−60o))−1y=−3sin⁡(2(x−60o))−1y = -3\sin(2(x-60^o))-1.
I re-did the graph:

upload_2016-8-15_2-24-35.png


Is this better?
 
  • #6
blue_leaf77
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Still incorrect. Start from ##f(x) = 3\sin(2(x-60^o))## which can be obtained by translating ##f(x) = 3\sin(2x)## to [left/right, it's your part to answer] by ##60^o## degrees.
 
  • #7
Still incorrect. Start from f(x)=3sin(2(x−60o))f(x)=3sin⁡(2(x−60o))f(x) = 3\sin(2(x-60^o)) which can be obtained by translating f(x)=3sin(2x)f(x)=3sin⁡(2x)f(x) = 3\sin(2x) to [left/right, it's your part to answer] by 60o60o60^o degrees.

Ok I have attempted the graph again:

The dotted curve is the original base function y = sinx, and I used it to help apply the transformations. The dotted lines show where the axes have been shifted.



upload_2016-8-15_20-0-46.png



Is this an improvement??
 
  • #8
blue_leaf77
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Nope.
Your first drawing is almost correct. It's just the negative sign in front of the sine function that needs to be removed. May be it's better to draw the functions resulting from each transformation. So, you start from ##y=\sin(2x)##, which is a harmonic function of period ##180^o## and amplitude 1. Then draw ##y=3\sin(2x)##. Followed by ##y=3\sin(2(x-60^o))## and finally ##y=3\sin(2(x-60^o))-1##. This is the only way we can spot in which step you went wrong.
 
  • #9
Your first drawing is almost correct. It's just the negative sign in front of the sine function that needs to be removed.
Okay, I have attempted the graph again, lets hope its an improvement at least :/

upload_2016-8-17_22-12-35.png
 
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  • #10
blue_leaf77
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Yes, that's the correct one.
 
  • #11
Yes, that's the correct one.
Thanks for the help! I really appreciate it :biggrin:
 

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