how to find amplitude and translations in a tan graph when period and coordinates are given?

Question

y=atan(pie/n t)+c

-has period of 4

find the value of n and hence find the values of a,t and c when the graph passes through (-1,3) and (4,0)

Answer 1

The coefficient of t is pi/n.  The usual period of a tangent graph is pi; pi divided by pi/n is n and since the period is 4,

n = 4.

 

The ordered pairs (4,0) & (-1,3) are (t,y), so

for (-1,3)

y = a•tan(pi/4•(-1))+c = 3 tells us that   a•tan(-pi/4) +c= 3

 

a•(-1) + c= 3...equation 1

 

From (4,0) we have y = 0 = a•tan pi + c

so a•(0) + c= 0....equation 2

 

Therefore (check mmy math) we find c = 0 & a = -3.

 

However, it seems to me that "a" is not an amplitude because that terminology does not apply except in sine/cosine graphs.