How do you graph #y=3 cos pi x#?

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Answer 1 · 2016-06-04T11:53:29

The graph is a series of periodic waves, with period 2 and amplitude 3. See explanation for Table {{x, y)}...,

The graph is a cosine wave-form, with period 2 and amplitude 3.

See the two graphs for visual effect.

Note that #|y(x)|<=3# and

#y(x+2)=3 cos (pi(x+2))=3 cos (pix+2pi)=3cos pix=y(x)#.

In one period #x in [0, 2]#, the graph passes through

# (0, 3), (1/4, 3/sqrt 2), (1/2, 0), (3/4, -3/sqrt 2), (1, -3), (5/4, -3/sqrt 2), (3/2, 0), (7/4, 3/sqrt 2) and (2, 3)#.,

graph{y=3 cos(4.1416x)}

Graph for one period, #0<=x<=2#:

graph{(y-3 cos(3.1416x))(x)(x-2)(y^2-9.4)=0[0 2]}}