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

1 Answer
Aug 2, 2018

Answer:

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.