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April 25th, 2016, 08:36 AM  #1 
Member Joined: Sep 2014 From: UK Posts: 82 Thanks: 1  Transforming a graph cos(x) to cos(2x60) in correct order?
So I was thinking cos(x) > cos(2x) > cos(2x60) is the correct order, since cos(x) > cos(x60) > cos(2(x60)) seems to me what would happen if I done the translation of 60 in x and then a stretch of 1/2 parallel to x. But the book gives me the order of the translation and then the stretch, and says it's cos(2x60). Does the order matter in this case? Last edited by skipjack; April 25th, 2016 at 11:15 AM. 
April 25th, 2016, 08:58 AM  #2 
Senior Member Joined: Dec 2015 From: holland Posts: 149 Thanks: 36 Math Focus: tetration 
Yes 2x  60 is not equal to 2(x  60).

April 25th, 2016, 10:24 AM  #3 
Member Joined: Sep 2014 From: UK Posts: 82 Thanks: 1  
April 25th, 2016, 10:25 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,966 Thanks: 2283 Math Focus: Mainly analysis and algebra 
$\cos x \longrightarrow \cos ( x 30) \longrightarrow \cos 2(x30) = \cos (2x60)$ There is no "correct order". 
April 25th, 2016, 10:48 AM  #5  
Member Joined: Sep 2014 From: UK Posts: 82 Thanks: 1  Quote:
The reason why I asked for 'correct order' is because the two translations in the book are (60 0) vector and 1/2 scale factor stretch parallel to the xaxis. There is no (30 0). Quote from the book: ''The curve of y = cos(x60) is obtained from that of y = cos(x) by a translation of (60 0). The curve of y = cos(2x60) is obtained from that of y =cos(x60) by a stretch of scale factor 1/2 parallel to the xaxis.'' It explicitly stated that it's getting the y = cos(2x60) from y = cos(x60) by stretch 1/2 parallel to x, which is not possible. Having an example from this book that is completely wrong and then beginning to doubt everything I learned is the worst, and I need to confirm that it's wrong with others because I can't trust myself. *Sigh* Last edited by skipjack; April 25th, 2016 at 11:10 AM.  
April 25th, 2016, 11:14 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,966 Thanks: 2283 Math Focus: Mainly analysis and algebra 
Yes, the book is wrong.

April 25th, 2016, 11:20 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,034 Thanks: 1393 
No, the book is correct.

April 25th, 2016, 11:36 AM  #8 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,966 Thanks: 2283 Math Focus: Mainly analysis and algebra 
The book could be correct if it is determined that we stretch from $x=0$ rather than anywhere else.
Last edited by v8archie; April 25th, 2016 at 11:52 AM. 
April 25th, 2016, 11:45 AM  #9 
Member Joined: Sep 2014 From: UK Posts: 82 Thanks: 1 
After a bit of research I found that the book apparently IS correct. cos(x) > cos(x60) > cos(2x60). Because in fact cos(x) > cos(2x) > cos(2(x60)) ...I'll just take it for a fact o_o 
April 25th, 2016, 12:14 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 18,034 Thanks: 1393 
The book is correct. It probably explains somewhere that the assumption v8archie refers to is $x=0$.


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