How do you find the maximum of the graph #y=-2cos(x-pi/2)#?

1 Answer
Feb 27, 2017

#((3pi)/2, 2)#

Explanation:

The maximum and minimum of any #cos# graph on its own will be #+1# or #-1#. It doesn't matter so much what's inside the #cos# function, only what's outside.

Multiply these by #-2#, the outside of the equation, to get maximum/minimum points of #-2# and #+2#.

The maximum is therefore #+2#.

To find at which point this occurs, work backwards.

#+2 = -2cos(x-pi/2)#

Divide both sides by #-2#

#-1 = cos(x-pi/2)#

Do a backwards #cos# (#cos^-1#) to get rid of the forwards #cos#

#cos^-1(-1)=x-pi/2#
#pi = x-pi/2#
#x = (3pi)/2#

Now we have our #x# and #y# values:

#((3pi)/2, 2)#