The portal has been deactivated. Please contact your portal admin.

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

In which quadrant does the angle โˆ’17๐œ‹/36 lie?

01:34

Video Transcript

In which quadrant does the angle negative 17๐œ‹ over 36 lie?

We begin by sketching the ๐‘ฅ๐‘ฆ-coordinate plane and labeling the quadrants one to four as shown. We recall that any angle in standard position is measured from the positive ๐‘ฅ-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 ๐œ‹ radians. So in a clockwise direction, we can mark on the angles negative ๐œ‹ over two, negative ๐œ‹, negative three ๐œ‹ over two, and negative two ๐œ‹.

The angle in this question has a denominator of 36. And as 18 is half of 36, we can rewrite negative ๐œ‹ over two as negative 18๐œ‹ over 36. This means that negative 17๐œ‹ over 36 lies between zero and negative ๐œ‹ by two. And we can therefore conclude that the given angle lies in the fourth quadrant.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.