How do you graph #y=-tan2x# and include two full periods?

1 Answer
Adam L.
Mar 20, 2017

Create a normal tan graph:
graph{tan(x) [-0.5, 6.29, -4, 4]}
(If you don't know how, then either think of how tan changes as the angle of the triangle increases from zero, or remember this chart:

#0# : #0#
#pi/4# : #1#
#pi/2# : undefined (goes off to infinity)
#(3pi)/4# : #-1 #
#pi# : #0#
Repeat this at least twice.)

Then compress it in the horizontal by a factor of two (because of the #2x# in the tan:
graph{tan(2x) [-0.5, 6.29, -4, 4]}
Then flip it on the vertical (because of the negative sign):
graph{-tan(2x) [-0.5, 6.29, -4, 4]}

The graph must show at least #pi#, since the period of #tan(x)# is pi, which was divided in two by the 2x inside the tan, then multiplied because you need to show two periods

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