How do you find the amplitude and period of #y=0.7tan(0.3x-1.8)#?

1 Answer
Nov 4, 2015

The amplitude does not exist/is undefined or however you want to say it. The period is #(20pi)/3#.

Explanation:

The equation can be written as #a sin(b(x-c)) + d#. For sin and cos (but not tan) #|a|# is the amplitude, #(2pi)/|b|# is the period, and #c# and #d# are the phase shifts. #c# is the phase shift to the right (positive #x# direction) and #d# is the phase shift up (positive #y# direction). In this case, you need to take out a #.3# inside of the parentheses. You then get #0.7tan(0.3(x-0.6))#. Now just follow the model above; the period is #(2pi)/.3# or #(20pi)/3#.
Note that tangent graphs do not have altitudes (they go from #-oo# to #oo#).