SOLUTION: Please help me graph a cotangent function y=cot(x-pi/4)-1/2 I understand how to get the period which is pi but the vertical aymptotes and x-intercept i'm having trouble with.

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me graph a cotangent function y=cot(x-pi/4)-1/2 I understand how to get the period which is pi but the vertical aymptotes and x-intercept i'm having trouble with.      Log On


   

Question 258870: Please help me graph a cotangent function y=cot(x-pi/4)-1/2 I understand how to get the period which is pi but the vertical aymptotes and x-intercept i'm having trouble with.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
So far I agree with:
period = pi
horizontal shift = pi/4 units right
vertical shift is 1/2 unit down
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There is a vertical asymptote at 3pi/4 and then every +pi and - pi units.
We can generally say 3pi/4 +- Kpi, K is an integer
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Set
(i) cot%28x-pi%2F4%29+-1%2F2+=+0
We want to find a number such that cot(x-pi/4) = 1/2.
It turns out 63.4 degrees is close.
63.4 degrees = 3.5222PI
So,
x-pi/4 = 3.5222pi
x = 3.27222pi
This is where a zero occurs.
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Now zero's occur at pi intervals, so in general,
we have zero's at
3.2722pi +- kpi, k is an integer.
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hope this helps