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]}

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