Understanding Phase Shift in Trigonometric Functions

[smashbrohamme]

Find the phase shift of a function.

Y=-5sin(x-pie/2)

The Phase shift is (pie/2)/1 which equals to pie/2. The correct answer is units to the right though..which is where I need clarification on.

My book said if phi is less than 0, it is too the left.. being -pie/2 wouldn't this indicate to the left?

Another example.

y=4cos(x+pie/2) once again phase shift is pie/2...but it is units to the left...units to left indicates phi...which is pie in this case..is negative...how is that possible?

It is easy to remember if it has a plus sign..it is units to the left...
negative sign ends up being units to the right...I just don't understand and if I don't truly understand than I won't remember it long term.

Thanks for your help.

Homework Equations

The Attempt at a Solution

 

[SammyS]

Find the phase shift of a function.

Y=-5sin(x-pie/2)

The Phase shift is (pie/2)/1 which equals to pie/2. The correct answer is units to the right though..which is where I need clarification on.

My book said if phi is less than 0, it is too the left.. being -pie/2 wouldn't this indicate to the left?

Another example.

y=4cos(x+pie/2) once again phase shift is pie/2...but it is units to the left...units to left indicates phi...which is pie in this case..is negative...how is that possible?

It is easy to remember if it has a plus sign..it is units to the left...
negative sign ends up being units to the right...I just don't understand and if I don't truly understand than I won't remember it long term.

Thanks for your help.

Does your book say something like:

For

\sin(x-\phi)\,,​

if \phi is positive then the shift is to the right,

if \phi is negative then the shift is to the left .​

?

If that's the case, then your \phi is π/2, which is positive.

 

[smashbrohamme]

ah, so they are factoring in that your equation sin(w-phi) can make two negatives into a positive...

 

[SammyS]

ah, so they are factoring in that your equation sin(w-phi) can make two negatives into a positive...

Yes.