How do you graph #p(t)=1/2cot(pi/4t)# over the interval #[-4,4]#?

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Answer 1 · 2018-08-02T16:07:10

See graph and explanation.

#p ( t ) = 1/2 cot (pi/4 t) = 1/2 cos ( pi/4 t )/sin ( pi/4 t )#,

#pi/4 t ne # asymptotic # k pi, k = 0, +- 1, +- 2, +-3, ...#

#rArr t ne 4 k #

# rArr t ne 0, +- 4, +- 8, ...#

The period = pi/(pi/4) = 4.

Graph for two periods, #t in [ - 4, 4 ]#,

sans asymptotic #t = 0, +- 4#:
graph{(2ysin(pi/4x)-cos(pi/4x))(x-4+0.0001y)(x+4+0.0001y)(x +0.0001y)=0[-4.4 4.4 -2 2]}