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Okay, this has been driving me crazy. When combining two given waves into a standing wave equation, how do you know which sign to put in front of the amplitude? All the examples I've been finding seem to contradict each other. Here are three examples from my textbook:

1. Incoming Wave:

y=4sin[2pi(t)-6pi(x)]

Reflected Wave:

y=-4sin[2pi(t)+6pi(x)]

Standing Wave:

y=-8cos3(pi)t*sin6(pi)x

---------------------------

2. Incoming Wave

y=-4sin[2pi(t)+6pi(x)]

Reflected Wave:

y=4sin[2pi(t)-6pi(x)]

Standing Wave:

y=8cos3(pi)t*sin6(pi)x

---------------------------

3. Incoming:

y=-8sin[2(pi)t-7(pi)x]

Reflected Wave:

y=8sin[2(pi)t+7(pi)x]

Standing:

y=16cos2(pi)t*sin7(pi)x

---------------------------

Help?!?

How do I know when it's positive or when it's negative?