Question Video: Determining the Quadrant in Which a Given Angle Lies

In which quadrant does the angle −242° lie?


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.

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