How do you graph #y=3csc(pi/2x)#?

1 Answer
PaulThePerson
Apr 28, 2018

The period is 4, and the amplitude is 3.enter image source here

Explanation:

The beginning coefficient of this problem indicates that it has an amplitude of 3. The vertices of each of the shapes will be at plus or minus 3. The amplitude can be calculated by taking the term #csc(pi/2x)# .
The normal amplitude of a trigonometric function is #2pi# so you divide #2pi# by #pi/2# to get 4. Because the #csc# function has a negative section and a positive section(for a lack of better explanation) , each of these sections will have a width of 2 between their asymptotes. An asymptote is on the y axis because there is no offset in the equation and the sine function has a value of 0 at #x=0#. Therefore, because #csc# is the inverse function of sine, there will be an asymptote at x=0.

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