Question

How do you graph `g(t)=2cot2t` and include two full periods?

Answer 1

See graph and details.

Explanation:

`g( t ) = 2 cot 2t = 2 ( cos 2t)/(sin 2t)`

`2t ne` any zero fo the denominator `sin 2t`

`rArr` asymptotic `t ne` asymptotic

`k ( pi /2 ), k = 0, +-1, +-2, +-3, ...`.

Period = common period of `sin 2t and cos 2t =(2pi)/2 = pi`.

See graph, depicting these aspects, for twp periods,

`t in [ - pi, pi ]`, sans asymptotic `t = +- pi/2`, in between..
graph{(y sin( 2x) - 2 cos (2x) )(x-1/2pi +0.0001y)(x+1/2pi +0.0001y)(x-pi +0.0001y)(x+pi +0.0001y)=0[-3.4 3.4 -7 7]}

The graph is not to uniform scale.