SOLUTION: need help graphing through at least one period and how to find amplitude, phase shift, vertical shift, period y=-2+csc((1/2)x+(pi/4))

Question 512396: need help graphing through at least one period
and how to find amplitude, phase shift, vertical shift, period
y=-2+csc((1/2)x+(pi/4))
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
need help graphing through at least one period
and how to find amplitude, phase shift, vertical shift, period
y=-2+csc((1/2)x+(pi/4))
**
standard form of equation for csc function: y=csc(Bx-C), period=2π/B, phase shift=C/B
For given equation:-2+csc((1/2)x+π/4))
B=1/2
Period=2π/(1/2)=4π
Phase shift=C/B=π/4/(1/2)=π/2 (to the left)
Vertical shift=2 units down
..
Graphing:
Without horizontal and vertical phase shifts,
you can plot the basic csc(x/2) curve with the following coordinates:
(0, asymptote), (π,1), (2π, asymptote), (3π,-1), (4π, asymptote)
shifting curve π/2 to the left:
(-π/2, asymptote), (π/2, 1), (3π/2, asymptote), (5π/2,-1), (7π/2,asymptote)
Dropping curve 2 units down: (final configuration)
(-π/2, asymptote), (π/2, -1), (3π/2, asymptote), (5π/2,-3), (7π/2,asymptote)
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