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.