How do you graph #y=-csc3theta#?

1 Answer
Feb 18, 2018

Answer:

See below.

Explanation:

#y=-csc3theta#

#=-1/sin(3theta)#

Let #x=3theta -> y=-1/sinx#

Consider: #lim_(x->0^+) -1/sinx = -oo#

and, #lim_(x->0^-) -1/sinx = oo#

This cycle is repeated for #lim_(x->npi^+) y# and #lim_(x->npi^-) y# #forall n in ZZ#

Note that #y# has local maxima of #-1# at #x=((2n+1)pi)/2 forall n in ZZ# and #y# has local minima of #+1# at #x=((4n-1)pi)/2 forall n in ZZ#

This can be represented graphically below.

graph{-1/sinx [-10, 10, -5, 5]}

Replacing #x# by #3theta# has the effect of decreasing the period by a factor of 3. As shown below.

graph{-1/sin(3x) [-10, 10, -5, 5]}

Hence, the graph above is the graph of #y=-csc(3theta)#
where #theta# is shown on the vertical axis.