How do you graph #5+8cos2x#?

1 Answer
Bharat K.
May 2, 2015

We have #f(x) = 5 + 8cos2x#

Let's first breakdown the above equation.
#cosx# is pretty simple to plot as a function of x (just a sinusoidal wave). Now, #cos2x# plot looks exactly same as #cosx# but it varies two times faster than #cosx# (see the plots below).

#cosx#

graph{cos(x) [-10, 10, -2, 2]}

#cos2x#

graph{cos(2*x) [-10, 10, -2, 2]}

Multiplying #cos2x# by #8# gives you the following plot
(changes the amplitude of the curve)
#8cos2x#

graph{8cos(2x) [-10, 10, -10, 10]}

Finally, adding #5# to #8cos2x# shifts the plot by 5 on the y-axis
#5+8cos2x#

graph{5+8cos(2x) [-10, 10, -6, 14]}

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