How do you graph #y=1/2cospix#?

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Answer 1 · 2017-06-06T12:29:59

Graph #cos(x)#, then increase frequency and halve the amplitude.

Start with the graph of #y=cos(x)#. The primary points required to adequately draw the graph are

#f(x)=cos(x)#

#cos(-(3pi)/2)=0 => (-(3pi)/2,0)#

#cos(-pi)=-1 => (-pi,-1)#

#cos(-(pi)/2)=0 => (-(pi)/2,0)#

#cos(0)=1 => (0,1)#

#cos((pi)/2)=0 => ((pi)/2,0)#

#cos(pi)=-1 => (pi,-1)#

#cos((3pi)/2)=0 => ((3pi)/2,0)#

These give the basic graph of #y=cos(x)#

graph{cos(x)[-5,5,-1.2,1.2]}

Next, the frequency will increase by #pi#, or a factor of just barely over three.

graph{cos(pi*x)[-5,5,-1.2,1.2]}

Finally, cut the amplitude of the function in half.

graph{1/2 cos(pi*x)[-5,5,-1.2,1.2]}