SOLUTION: Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1? I need to show work

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1? I need to show work      Log On


   



Question 1042538: Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1?
I need to show work

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The amplitude is normally +1+, so you
need a factor of +2+
The midline is normally +0+, so you need
to add +1+ to the function
--------------------------
So far, it looks like
+f%28x%29+=+2%2Acos%28+k%2Ax+%29+%2B+1+
------------------------
You ar told that:
when +x+=+pi%2F3+ then the cosine has gone
through an entire period, so it must be true:
+k%2A%28+pi%2F3+%29+=+2%2Api+
+k+=+6+
So, the function must be:
+f%28x%29+=+2%2Acos%28+6x+%29+%2B+1+
Here's a plot of 2 periods in both directions from
+x+=+0+. It is plotted from +x+=+-2%2Api%2F3+ to
+x+=+2%2Api%2F3+

( note that +f%28pi%2F3%29+=+3+ as it should )