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The range of a cosecant function is (-∞,-9] ∪ [5,∞). The equations of two consecutive asymptotes of the function are x = 0 and x=2π. The function is not a reflection over the x-axis.

What is the equation of this cosecant function?

Mar 19, 2020

#1
+111360
+3

The  form we  seek is

y = Acsc ( Bx)  + C

A =  the amplitude  =  [5 - - 9] / 2  =  14/ 2  =  7

C  =  the midline  =  [ 5-9]/2 = -4/2 =   -2

The period  =  2pi -  0  =  2pi

And

B  =  normal period  /  our period         =    pi  / [ 2pi]   =   1/2

So....our equation  is

y =  7csc ( (1/2)x)  - 2

Here's  the graph  :  https://www.desmos.com/calculator/qpwj6t9ook

Mar 19, 2020
#2
+2

Okay, I know that this might sound really dumb, but when I saw that you answered my question, I got very excited because whenever I need math help, I always see your answers and they're the most helpful. I just appreciate that a lot, so thank you.

Guest Mar 19, 2020
#3
+109497
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No, it does not sound dumb. I am quite sure that Chris appreciations your comments just as all answerers do.

If you become a member your appreciation will be more recognized

Members who make a good name for themselves definitely get preferential treatment.

Mar 19, 2020
#4
+111360
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Thanks, Melody  and Guest   !!!!

Mar 19, 2020