Video Transcript
In which quadrant does the angle
negative 242 degrees lie?
Remember, if we take the coordinate
plane, we can split it into four quarters which are called quadrants. We label these in a
counterclockwise direction, and we use Roman numerals to do so. We say that this quadrant is the
first quadrant. We have the second over here. The third then lies down here. And this is the fourth
quadrant. So in which quadrant does the angle
negative 242 degrees lie?
Well, to find out, we’re going to
begin by adding the initial side of our angle onto the diagram. The vertex of our angle has to lie
at the origin and its initial side must be located on the positive 𝑥-axis as
shown. Since the angle is negative, we
need to travel in a clockwise direction. We’ll do this in intervals of 90
degrees. 90 degrees takes us to this line
here. Then another 90 degrees takes us
half a turn. It takes us 180 degrees. And our terminal side would lie on
the negative 𝑥-axis. If we were to continue another 90
degrees, that would take us all the way to 270 degrees.
And in fact, of course, since we’re
traveling in a clockwise direction, they should all be negative. But we only wanted 242 degrees. And so we’re not going to quite
complete that last quarter of a turn. We can therefore say that the angle
negative 242 degrees lies in the second quadrant.
