Expert: Ahmed Salami - 5/7/2010

Question
QUESTION: Assalamalaikum

Sir,
I had this doubt while preparing for SAT MATH LEVEL 2
Here's the link
http://oldfacebookrox.t35.com/Barron%5C%27s%20Maths.bmp

How do you find the equation of the graph? Please explain briefly.
Thnks a ton

ANSWER: Hi Abdul Quadeer,
The graph shows a peak-to-peak value of 1 meaning that the amplitude is 0.5 and it appears to be a basic cosine function turned upside down and moved up 0.5 units.
The basic cosine function with amplitude 0.5 is y = 0.5cosx
Turning upside down makes it y = -0.5cosx
Moving it up by 0.5 units makes it y = -0.5cosx + 0.5
And so,
y = 0.5 - 0.5cosx
 = 0.5(1 - cosx)

But of course it can be considered in other ways, depends on who's doing it.

Regards

---------- FOLLOW-UP ----------

QUESTION: Sir,
The answer given in my book is 1-2y=cos2x,
from where does the 2 come in 2x?

Answer
Hi,
Yes, its 2x and not x. My mistake.
The basic cosine function y = cosx has a period of 2π. The graph shown here has a period of π which indicates a scaling factor of 2. Actually, y = cos2x has a period half of that of y = cosx and not twice its period as one might first think. The graph of y = cos(x/2) has a period of 4π.
Hope you understand it.

Regards