SOLUTION: Find an equation of a tangent function with period 3𝜋 and phase shift pi/2

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Question 1195467: Find an equation of a tangent function with period 3𝜋 and phase shift pi/2
Found 3 solutions by Alan3354, greenestamps, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of a tangent function with period 3𝜋 and phase shift pi/2
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y = tan((x/3) - pi/6)
or
y+=+tan%28%28x+-+pi%2F2%29%2F3%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A general form of a tangent function is

y=a%2Atan%28b%28x-c%29%29%2Bd

a determines the steepness of the graph
the period is (pi)/b
c is the phase (horizontal) shift
d is the vertical shift

This problem puts no requirement on the steepness of the graph or the vertical shift, so we can let a=1 and d=0, giving us

y=tan%28b%28x-c%29%29

This problem says the period should be 3pi, so

pi%2Fb=3pi
b=%28pi%29%2F%283pi%29=1%2F3

And the phase shift is given as pi/2.

So b=1/3 and c=pi/2:

ANSWER: y=tan%28%281%2F3%29%28x-pi%2F2%29%29

That can be written in many forms; for example,

y=tan%28%281%2F3%29x-%28pi%2F6%29%29

Answer by ikleyn(52792) About Me  (Show Source):