SOLUTION: I'm in pre calculus and I need help with solving a problem. It is y=cot(x-pi/4) I need to find the period, frequency, phase shift, vertical shift, amplitude, and the asymptotes.

Question 993701: I'm in pre calculus and I need help with solving a problem. It is y=cot(x-pi/4) I need to find the period, frequency, phase shift, vertical shift, amplitude, and the asymptotes.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is y=cot(x-pi/4)

below is the graph of the equation of y = cot(x) and y = cot(x - pi/4).

$$$

the graph of y = cot(x) is in orange.
the graph of y = cot(x - pi/4) is in black.

you will see that the graph of y = cot(x - pi/4) is shifted to the right of the graph of y = cot(x) by pi/4 radians.

the normal interval of the cotangent function is 180 degrees, or pi.

this means the graph repeats every 180 degrees, or every pi radians.

interval shown for y = cot(x) is 0 to pi.
interval shown for y = cot(x - pi/4) is pi/4 to 5pi/4.

the general form of a sinusoidal type wave is:

y = a * sin(b * (x-c)) + d or:
y = a * cos(b * (x-c)) + d or:
y = a * tan(b * (x-c)) + d or:
y = a * cot(b * (x-c)) + d or:

a is the amplitude
b is the frequency
c is the horizontal shift
d is the vertical shift.

sin and cos are sinusoidal type of wave with a period of 360 degrees because their pattern repeats every 360 degrees.

tan and cot are a sinusoidal type of wave with a period of 180 degrees because their pattern repeats every 180 degrees.

you want to find the period, frequency, phase shift, vertical shift, amplitude, and the asymptotes for the equation of y = cot(x - pi/4).

the period is 180 degrees, or pi radians.
the frequency is 1 because it is now shown.
the phase shift is the same as the horizontal shift which is pi/4.
the vertical shift is 0 because it is not shown..
the amplitude is 1 because it is not shown.
the asymptotes are at pi/4 and 5pi/4.

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