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>> This is your math gal
Julie Harland.
Please visit my website
at yourmathgal.com where all
of my videos are organized
by topic.
All right we're going
to solve this trig equation,
sine of x equals -.315
and we're trying
to find all angles
in the interval zero
to 360 degrees.
So first of all,
make sure that your calculator
is in degree mode.
[ Pause ]
Otherwise you'll get it
in radiance.
Okay? That's
because we're looking
for something
between zero and 360.
Now one way to go
about this is that angle,
and this isn't necessarily
going to be the angle I want
for my final answer
between zero and 360
because there are infinitely
many angles, right?
Where if you take the sine you
can get -.315.
So one possibility is you do
the sine inverse
of .315, okay?
So you can plug
that into your calculator
and we're going to round
that to the nearest tenth
of a degree.
And let's see, so I'm putting
that in and I get -18.4.
So the first thing I notice is
that's not an angle
in where I want my answer
to be.
I want my answer to be
in between zero
and 360 degrees.
So how would I find a
co-terminal angle with this
so it's between zero
and 360 degrees?
Remember you can add
or subtract 360 degrees
to get a co-terminal angle.
So if I add 360 I'll get
something in the range I want.
So if I do -18.4 degrees plus
360 what does that give you?
Let me do that.
I get 341.6 degrees
and now I do have an angle
in the correct range.
All right so let's say I'm
going to write my
answers here.
I know that's going to be one
of the solutions,
341.6 degrees.
Now to make sure,
simply compute the sine
of 341.6 degrees
in your calculator
and make sure it comes out to
about -.315.
I've rounded here so you know,
might not come out exactly.
I'm going to do
that real quickly.
So if you want to know
for sure if that's about,
that's correct,
let's just plug in,
so in other words the check
in other words.
What is the sine
of 341.6 degrees?
And let's see when I plug it
in I get -.316, so yeah we're
in the ballpark.
It's because of the rounding
that it might not come
out exact.
All right so just make sure
you understand
that would be true.
All right now how would we
find where the other angle is?
Because there's two place
where the sine is negative.
It's in the first, I mean it's
in the third
and the fourth quadrant.
So in other words,
I know there's this one
over here and that's,
you know, 341.6 degrees going
all the way around.
And in fact,
this right here was the -18.4.
Now I'm not going to worry
about it's negative or not,
but that's basically 18.4
degrees, right?
This area right there,
or this angle not considering
whether it's positive
or negative.
So there should be another one
over here.
And how could I get that?
In other words,
how would I figure
out what that is?
Well, I have 180 degrees plus
this extra piece,
and this piece is the same
as that piece over there.
So I have 180 degrees, right?
Plus that extra piece
which is 18.4 degrees.
Or 198.4 degree.
Rather than memorize it,
I always like to look
at the picture
and you're just doing a little
problem solving
to figure it out.
All right?
Because this should have the
same sign, if you look
at it, right?
The same sort of triangle.
The Y coordinate's negative
in both cases.
The radius here
or the hypotenuse is the same.
So my other one looks
like it's going
to be 198.4 degrees,
and remember it doesn't matter
the order you write
your solutions.
If you like to write the
smaller number first, awesome.
No problem.
But let's just do a quick
check that may--
so in other words,
in your calculator,
checking your calculator
to see what the sine
of 198.4 degrees,
make sure you are going to get
up to around -.35.
So I'm going to do
that right now.
I'm putting in 198.4.
Do it with me.
Make sure it's in degree mode.
And I got approximately -.316.
Again, yup close.
So that's how you would do
this problem.
Little bit tricky
because when you do the,
you know, inverse sign,
you don't get something
in the range you're looking
for between zero
and 360 degrees.
This is your math gal
Julie Harland.
Please visit my website
at yourmathgal.com where all
of my videos are organized
by topic.