Question 454197: how do i graph y=5cot((x/3)-(pi/4))
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do i graph y=5cot((x/3)-(pi/4))
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Standard form for Cotangent function: y=Acot(Bx-C), with period=π/B, phase shift=C/B, A is just a multiplier that stretches the curve vertically.
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y=5cot((x/3)-(π/4))
period=π/B=π/(1/3)=3π
1/4 period=3π/4
Phase shift=C/B=(π/4)/(1/3)=3π/4 (to the right)
Graphing:I don't have the means to graph it for you, but this is how you can do it.
On the x-axis make a tick mark at 3π/4 and 4 more tick marks after that spaced 1/4 period apart. You now should have tick marks at 3π/4, 6π/4, 9π/4, 12π/4 and 15π/4. Note this covers one full period=3π. At the first tick mark draw an asymptote, x=3π/4. At the last tick mark on the right, draw another asymptote, x=15π/4. At 6π/4, 1/4 into the period, the cotangent function, y=1*5(multiplier)=5. At 9π/4, half a period, y=0. At 15π/4, 3/4 into the period, y=-1*5=-5. You now have the following points to graph the curve:
(15π/4,asymptote),(6π/4,5), (8π/4,0), (12π/4,-5), and (15π/4, asymptote)
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