How do you graph # y=cos(x+pi/2)#?

1 Answer
Feb 21, 2018

Answer:

Shift points on the graph of #y=cos(x)# to the left by #pi/2# units, plot a full period, and plot further using the fact that cosine is periodic and reflected over the y-axis if necessary.

Explanation:

Shift some points on the graph of #y=cos(x)# to the left #pi/2# units (subtract #pi/2# from the x-coordinate) .

#(0,1)# becomes #(-pi/2,1)#
#(pi/2,0)# becomes #(0,0)#
#(pi,-1)# becomes #(pi/2,-1)#
#((3pi)/2,0)# becomes #(pi,0)#
#(2pi,1)# becomes #((3pi)/2,1)#

Plotting these points will yield a full period for #y=cos(x+pi/2)#. From #((3pi)/2,1)#, the graph repeats itself. graph{y=cos(x+pi/2) [-10, 10, -5, 5]}

Also, recall that #cos(x)# is an even function ( #cos(-x)=cos(x)#) , meaning it has y-axis symmetry. Reflect these points over the y-axis to obtain a larger portion of the graph for negative values of #x.#