How do you sketch the graph of #f(x)=arccos(x/4)#?

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Answer 1 · 2018-08-03T04:23:54

See graph, with details.

#y = arccos ( x/4 ) in [ 0, pi ]#

The graph is restricted to be like this.

Inversely,

#x = 4 cos y in [ - 4, 4 ]# and the waveform, in the y-direction, is

understandable. Yet, the graph is blocked,

and the the y- periodicity becomes incognito.

See graph.
graph{(y-arccos (x/4))=0}
For contrast, see the wholesome inverse graph of # x = 4 sin y#

that is identical with the piecewise wholesome

#y = (cos)^(-1)(x/4) = kpi + (-1)^k arcsin (x/4),#

#k = 0, +-1, +-2, +-3,...#:
graph{(x-4 cos y)(x-4 +0.001y) (x+4 +0.001y) = 0[ -5 5 -20 20]}

This graph is not on uniform scale, for better visual effect.