How do you graph #y=1/3 tanx# and include two full periods?

1 Answer
Aug 13, 2018

Answer:

See double-cycle graph.

Explanation:

#y = 1/3 tan x = 1/3 (sin x/cos x),#

#x ne# ( zero of denominator ) #kpi, k = 0, 1, +-2, +-3, ...#.

Tthe period of #oo#-arm tan wave #= pi#.

Amplitude of a wave of infinite length, about the axis y = 0 is pi/2.

x-intercepts ( zeros of the numerator )#

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

See #oo#-arm tan waves, for two cycles, between ( asymptotic )

#x = +- pi#. , .
graph{(3ysin x - cos x )(x+pi+0.0001y)(x-pi+0.0001y)=0[-5 5 -2.5 2.5]}