SOLUTION: State the period and 2 consecutive asymptotes of the graph:\ a) y= csc x/3 b) y= 3 cot pi(x)/2

Question 454698: State the period and 2 consecutive asymptotes of the graph:\
a) y= csc x/3
b) y= 3 cot pi(x)/2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
State the period and 2 consecutive asymptotes of the graph:\
a) y= csc x/3
b) y= 3 cot pi(x)/2
..
a) Standard form for csc function: y=Asec(Bx-C), with period =2π/B, phase-shift=C/B, A=multiplier which stretches curve vertically.
For given function, y= csc x/3, A=1, phase-shift=0
period=2π/B=2π/(1/3)=6π
Asymptotes: x=0 and x=3π (Note that at 0, and every half period thereafter, sin x, the reciprocal of csc x, is approaching 0, so csc x is approaching infinity at these points.)
..
b) Standard form for cot function: y=Acot(Bx-C), with period =π/B, phase-shift=C/B, A=multiplier which stretches curve vertically.
For given function, y=3 cot pi(x)/2, A=3, phase-shift=0
period=π/B=π/(π/2)=2
Asymptotes: x=0 and x=2 (Note that at 0, and every period thereafter, tan x, the reciprocal of cot x, is approaching 0, so cot x is approaching infinity at these points.)
RELATED QUESTIONS
Graph one period the function y = 3 csc(1/2)x Show the asymptotes and the extrema.... (answered by josmiceli,MathLover1)

Please state the period and 2 consecutive asymptotes of the two graphs. 1. y=... (answered by lwsshak3)

1. Find the values of the remaining functions if tan=1/4, sin<0 sin= cos= csc= sec=... (answered by MaxWong,MathTherapy)

Which equations have a corresponding graph identical to the graph of y=tan(x) A)... (answered by MathLover1)

I.Find the amplitude, period, and phase shift of the function II. Sketch the graph A. (answered by lwsshak3)

Determine the asymptotes of this function: y = -csc(pi x/2 + pi/2) Here is my... (answered by jsmallt9)

if f(x)=3 tan 2x, state the following. a. the period of the function b. the equation... (answered by stanbon,Edwin McCravy)

how to graph y=2/3 csc (x-... (answered by Theo)

how to determine and graph the amplitude,period, frequency, and phase shift of each... (answered by stanbon)