How do you find the amplitude, period, vertical and phase shift and graph #y=3+1/2cos(theta+pi)#?

1 Answer
Jan 18, 2017
  • amplitude #=1/2#

  • period #=2 pi#

  • vertical shift #=+3#

  • phase shift #=-pi#

Explanation:

#y=3+1/2cos(theta+pi)#

maybe start by re-writing it as

#y-3 = 1/2cos(theta+pi)#

So:

y is shifted up by 3, the vertical shift, and #theta# is shifted left by #pi#

#implies Y = 1/2cos(Theta)#, where # Y = y - 3, Theta = theta + pi#, and the function #cos(Theta)# has period #2 pi# and #1/2cos(Theta)# has amplitude #1/2#.

We conclude that:

  • amplitude #=1/2#

  • period #=2 pi#

  • vertical shift #=+3#

  • phase shift #=-pi#