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

In which quadrant does the angle −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 𝑥𝑦-coordinate plane and labeling the quadrants one to four as shown. We recall that any angle in standard position is measured from the positive 𝑥-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.