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>> This is a continuation of solutions
to the trig test 2 review.
Okay here's 60 graph Y equals sine, of X plus pi over 4.
Now there's nothing in front of the sine so we have an amplitude
of one, there's no stretching the amplitude it's going
to be one and the period notice there's no coefficient
of X except one so the period is the same
as the regular sine function which will be two pi.
And then the phase shift if we have X plus pi over 4
so the phase shift, all right,
basically it's the opposite sine,
if this is a plus it's a shift to the left,
this number of spaces so it's going to be pi over 4 units
to the left so remember if this is a plus pi over 4 it's going
to shift to the left, here's one way to remember that,
how would you get this back to just plain old zero well
if you put a negative pi over 4 in for X all right so if you put
in a negative pi over 4 in you can think
about that's the negative you're going to the left.
Okay there's a couple ways to do this,
you could graft the sine function
and remember here are the basic in green over her
on the left are you know the important numbers
that you're going plot important order of pairs you're going
to plot on the sine function
and what you could do is just shift everything pi over 4
or what we could do is make a table and for X and Y
so I'm going to do X and then the sine of X plus pi over 4
and what happens when you have just a phase shift is all the X
values are just shifted pi over 4 so if you take theta over here
and you just subtract pi over 4 and you keep the value
of the sine the same watch what happens,
instead of zero it's negative pi over 4 and then you're going
to have to do pi over 2 minus pi over 4 so you're subtracting pi
over 4 from each of these X values over here
that I've written as data so that's going to be pi over 4
and then you do pi minus pi over 4, that's going to give a 3 pi
over 4 and we're going to have 3 pi over 2 minus pi
over 4 I think that's...those are going up by 2 pi over 4
so that's going to be 5 over 4 and the last one 2 pi minus pi
over 4 that's going to be 7 pi over 4.
So I've shifted all the X values right, to the left
and all the Y values should stay the same.
Oops, this is supposed to be a zero at the bottom here,
sorry it's a negative 1,
I'm sorry I'm getting confused here...zero,
negative 1 and zero.
So if we graph it...this is a little bit trickier,
so I've got to start off at negative pi over 4 zero
so let's say this is 2 pi, okay, so the sine function is going
to be shifted, is going to start here and end right here.
Okay, so I'm going to make the extra marks here in between,
that makes it a little bit easier, okay.
And the amplitude still one so remember you're going
to break this up into four pieces, so there's 1, 2,
this is half way in there, in the middle,
right and this is going to go up one assuming that's the unit
of one and then in between here were going to go down one
and there's our sine function shifted pi over 4 to the left.
Now we could do the same thing over here,
it's going to go down; back up
and ending right here to show 2 periods.
All right, so there we go and if you were going
to label these it's kind of *** this graft
but you could still label, this is pi, etcetera right here
and let's see this is negative pi and that's negative 2 pi,
etcetera and there's our graph and again you could verify
that these are the right order pairs, negative pi over 4 zero,
so you go negative pi over 4 zero and then you go pi over 4,
you're going up one, 3 pi over 4, you're at zero, etcetera.
So it's always good to verify at the end all right
so that's the graph of Y equals sine of X plus pi over 4.