How do you find the amplitude, period, and shift for y=4tan2(x-pi/2)?

1 Answer
Dec 15, 2015
  • "Amplitude" = abs(a) = 4
  • "Period" = pi/b = pi/2
  • "Phase Shift" = c/b = pi/2

Explanation:

Here's one way to write a generic tangent function that has been transformed in some way.

f(x) = atan(bx-c) + d

In this scenario:

  • "Amplitude" = abs(a)
  • "Period" = pi/b
  • "Phase Shift" = c/b

For your specific problem, the coefficient b has already been factored out, meaning the problem is a bit easier:

f(x) = atan(b(x-c/b)) + d

The values are identical, but a bit easier to spot:

  • "Amplitude" = abs(a) = 4
  • "Period" = pi/b = pi/2
  • "Phase Shift" = c/b = pi/2

If this function was a sine or cosine function, the period would be (2pi)/b instead.