Question 665614: Sketch one full cycle of y=cot(3x-pi/2)+5.How do I find the points after I get the left and right asymptote,I need 5 points,I know one is pi/6 for the left and the right is 3pi/6.But I am not sure how to find the remaining 3 middle points.And I also know the amp,flip,vertical shift and period.
help me out if you can
thank you
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! y=cot(3x-pi/2)+5
equation of cot function: y=cot(Bx-C), period=π/B, phase shift=C/B
For given trig function: y=cot(3x-pi/2)+5
B=3
Period=π/B=π/3
1/4 period=π/12
Phase shift=C/B=(π/2)/3=π/6 (shift to the right)
..
Graphing:(3 steps) (x-axis in radians, y-axis in units)
coordinates of basic cot curve cot3x for one period:[0,π/3]
(0,asymptote), (π/12,1), (π/6, 0), (3π/12,-1), (π/3, asymptote)
..
phase shift π/6 to the right: (add π/6≈.524 to x-coordinate)
(0.524,asymptote), (.786,1), (1.048, 0), (1.309,-1), (1.571, asymptote)
..
bump up curve 5 units (final configuration)(add 5 to y-coordinates)
(0.524,asymptote), (.786,6), (1.048, 5), (1.309,-4), (1.571, asymptote)
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