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
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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.)
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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.)
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