SOLUTION: Graph one period the function y = 3 csc(1/2)x Show the asymptotes and the extrema. Thank you!

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Question 1130301: Graph one period the function y = 3 csc(1/2)x Show the asymptotes and the extrema.
Thank you!
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the plot:
+graph%28+600%2C+400%2C+-12%2C+12%2C+-20%2C+20%2C+3%2A%28+1%2Fcos%28+x%2F2+%29%29%29+
It looks like one period of +x%2F2+ would be +-pi%2F2 to +3pi%2F2+
so then:
+x%2F2+=+-pi%2F2+
+x+=+-pi+
and
+x%2F2+=+3pi%2F2+
+x+=+3pi+
which is what I see
The asymptotes are at +pi+ and +-pi+

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+3csc%28x%2F2%29 Show the asymptotes and the extrema.
y+=+3%281%2Fsin%28x%2F2%29%29

+graph%28+600%2C+600%2C+-30%2C+30%2C+-10%2C+10%2C3%281%2Fsin%28x%2F2%29%29%29+

vertical asymptote x=2pi%2An where n is an integer
y+=+3csc%28x%2F2%29 is asymptotic to x+=+0
y+=+3+csc%28x%2F2%29+is asymptotic to x+=+2pi+%282n+%2B+1%29
y+=+3+csc%28x%2F2%29+is asymptotic to x+=+4pi%2An
asymptote:
if n=0, x+=+2pi+%282%2A0+%2B+1%29-> x+=+2pi+
if n=0, x+=+4pi%2A0->x=0
if n=1, x+=+2pi+%282%2A1+%2B+1%29-> x+=+6pi+
if n=1, x+=+4pi%2A1->x=4pi
and so on




period 2pi%2Fb ,and b=1%2F2->2pi%2F%281%2F2%29=4pi
amplitude: none
max3csc%28x%2F2%29+=+-3 at x+=+4pi%2A+n+-+pi for integer+n
min3csc%28x%2F2%29+=+3 at x+=+4pi%2An++%2B+pi for integer n