How do you graph #-2tan3(x - 30) + 1#?

1 Answer
A. S. Adikesavan
Jul 29, 2018

See graph and details.

Explanation:

#y = - 2 tan (3 ( x - pi/ 6 ) ) +1#, asymptotic

#3 ( x - pi/ 6 ) ne { ( 2 k + 1 ) pi/2 }, k = 0, +-1, +-2, +-3, ...#

#rArr x ne { ( 2 k + 2 ) pi/6 } = { 2k ( pi/ 6 ) } ={ k (pi/3) }#

The period = the period of #tan 3x = pi/3#. See graph, with

asymptotes.
graph{(1/2(y-1)cos(3(x+pi/4))+sin(3(x+pi/4)))(x-1/3pi+0.0001y)(x+1/3pi+0.0001y)(x-2/3pi+0.0001y)(x+2/3pi+0.0001y)(x-pi+0.0001y)(x+pi+0.0001y)=0[ -4 4 -2 2]}

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