How to plot the graph of #f(x)= 10 cos 3x#?

1 Answer
Gió
Jul 1, 2015

Your function is a cosine function with amplitude #10# and period #2/3pi#.

Explanation:

The graph of your function is the same as the one from a "normal" cosine BUT:
1] Amplitude will be #10#;
2] Period will be: #period=(2pi)/color(red)(3)# using the #3# in front of the #x# in the argument of your #cos#. This means that your #cos# is "squeezed", completing an entire oscillation between #0# and #2/3pi# instead of between #0# and #2pi#!

Graphically:
#y=f(x)=10cos(3x)#
graph{10(cos(3x)) [-28.88, 28.86, -14.43, 14.45]}

Where you can see the outline of a normal #cos# function but with amplitude of #10# and period #2/3pi=2.09 rad#

I add another plot, easier to "see" (I hope!):
enter image source here

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