Question Video: Determining What Quadrant a Given Angle Lies in Mathematics • 10th Grade

In which quadrant does the angle β17π/36 lie?

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Video Transcript

In which quadrant does the angle negative 17π over 36 lie?

We begin by sketching the π₯π¦-coordinate plane and labeling the quadrants one to four as shown. We recall that any angle in standard position is measured from the positive π₯-axis. If the angle is positive, we measure in the counterclockwise direction. And if the angle is negative, as in this case, we measure in the clockwise direction.

We know that a full turn is equal to 360 degrees or two π radians. So in a clockwise direction, we can mark on the angles negative π over two, negative π, negative three π over two, and negative two π.

The angle in this question has a denominator of 36. And as 18 is half of 36, we can rewrite negative π over two as negative 18π over 36. This means that negative 17π over 36 lies between zero and negative π by two. And we can therefore conclude that the given angle lies in the fourth quadrant.