Heaviside/step function question

[missavvy]

Homework Statement

Hey so this is a really trivial question.

f(t) = { 0, 0<= t < pi
{ -sin3t, t>=pi

Just having trouble properly shifting this!

The Attempt at a Solution

f(t) = -u_pi(t)sin(3t)

= -u_pi(t)sin[3(t-pi+pi)]

= u_pi(t)sin[3(t-pi+pi)]

How do I take the +pi out?
I know it should end up as:

u_pi(t)sin[3(t-pi)]

I just don't really understand how from my last step.
thanks for reading!

 

[vela]

Homework Statement

Hey so this is a really trivial question.

f(t) = { 0, 0<= t < pi
{ -sin3t, t>=pi

Just having trouble properly shifting this!

The Attempt at a Solution

f(t) = -u_pi(t)sin(3t)

= -u_pi(t)sin[3(t-pi+pi)]

= u_pi(t)sin[3(t-pi+pi)]

What happened to the minus sign?

How do I take the +pi out?
I know it should end up as:

u_pi(t)sin[3(t-pi)]

I just don't really understand how from my last step.
thanks for reading!

Hint: 3(t-pi+pi)=3(t-pi)+3pi