Question

Write an equation for the given function given the period, phase shift, and vertical shift.
tangent function, period=1/3 pi, phase shift= 1/4 pi, vertical shift= -5

Answer 1

The answer is y=tan(3theta+3/4pi)-5 I just don't know how to find the 3 and 3/4pi of this equation.

Answer 2

tangent repeats every Pi radians (unlike sin or cos which repeat every 2pi)

if we call the period T, phi= phase shift, and theta is t (for easy typing)

tan ( pi/T * (t + phi) )
is the "generic" form
normally T is pi and phi=0 and you get the standard form tan( t)

with T= pi/3 , pi/T becomes 3/pi *pi =3
also, with phi = pi/4, we get
tan (3*(t+pi/4) )
or
tan(3t + 3 *pi/4)

Answer 3

Omg thank you, I was using the 2pi formula thingy instead of just pi

Answer 4

yes, tangent is different.