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This video is provided as supplementary material
for courses taught at Howard Community College, and in this video
I want toshow how to sketch angles in standard position,
and specifically I'm going to deal with angles
in degree measure. I'll do separate video with angles
in radians. So if I'm going to sketch angles,
I want to start with a coordinate plane.
I'll have an x-axis and y-axis.
And an angle in
standard position is going to begin on the positive side
of the x-axis and go counter-clockwise
around the origin. So if it travels anywhere from zero degrees
up to 90 degrees, it's going to stay in the first quadrant.
For the next 90 degrees, from 90 degrees to 180 degrees,
it will be in the second quadrant. After that, the next 90 degrees
will go through the third quadrant
up until 270 degrees. And after that,
up to 360 degrees, it will be in the fourth quadrant.
So let's say we're told to sketch an angle of
110 degrees in standard position.
So we're going to start out in standard position, meaning we're on
the positive side of the x-axis and we're going to move
110 degrees counterclockwise. So the first ninety degrees
will go through the first quadrant. We want 110, so we have 20 degrees more
to go.
So we're going to go through the first quadrant and then continue part way
into the second quadrant for the remaining 20 degrees.
And we'll end up
with a rough sketch, that's all we're looking for, of an angle of 110 degrees.
Now let's say we want to go further. Let's say we'll go 315 degrees.
So now we're going to go 90 degrees in the first quadrant,
another 90 degrees for total of 180 through the second quadrant,
another 90 degrees for 270
through the third quadrant. After the 270 degrees
we still have 45 degrees more to go.
So that will take us halfway through the fourth quadrant.
So an angle of 315 degrees.
is going to look something like this, not quite a full circle,
a full circle would be 360.
Now we can also go more than 360 degrees.
We could go, let's say, 460 degrees.
So if we do that, we're going to go
a full 360 degrees around
the origin. And then we need to go 100 degrees more.
So we'll go 90 degrees through the first quadrant
and 10 degrees after that
into the second quadrant, and we'll have an angle of
460 degrees. Let's do an angle even bigger.
Let's say I want 800 degrees.
So this one is going to go
once around -- that's 360 -- and then once more,
another 360, which would be a total 720,
and after the 720 degrees, we need 80 degrees more
to make 800. So we'll go
80 degrees more That will keep us
in the first quadrant but towards the top of it.
So this would be a rough sketch of an angle
of 800 degrees.
Now we can also have negative angles. So I'll clean this up
and we'll do some negative angles. Once again, I'll draw a
coordinate plane, the x-axis and the y-axis,
and I'll put in zero degrees,
90, 180, 270,
360 and
the quadrants, 1, 2, 3,
and 4. So let's say we want an angle
of -35 degrees. This will start in the standard position,
it's going to start on that positive side of the x-axis,
but instead of going counterclockwise,
it's going to go clockwise. So we want to go
-35 degrees. Well, anywhere
up until -90 degrees is going to stay in the fourth quadrant.
So we'll just go -35 degrees
and that would give a sketch of the angle.
Let's say we want a more negative angle, like -210 degrees.
So we go -90,
-90 again,
That takes us to -180. We need 30 more.
So we'll go -30 degrees. We're in the second quadrant,
and that would be an angle of -210 degrees.
And as with positive angles, negative angles can also be greater than
360 degrees.
So let's do -480 degrees.
So I'm going to go clockwise
a full time around the origin -- that's 360 degrees --
I still have a 120 degrees to go.
So I'll continue going clockwise. 90 degrees
will take me through the fourth quadrant. I need 30 degrees more,
so I'll end end up in the third quadrant.
So this would be a negative angle, -480 degrees.
So that's basic concept. I'll do another video with radians.
It's the same idea, but I wanted to separate the videos.
Take care, I'll see you soon.