Question

How do we represent one time around the circle (in the positive direction) in degrees? How many times around the circle is represented by 720∘? What positive degree measure arrives at the same place on the unit circle as negative 90 degrees?

Answer 1

One time around the circle in the positive direction is represented by 360 degrees. This is because a circle is divided into 360 equal parts or degrees.

To determine how many times around the circle is represented by 720 degrees, we divide 720 by 360:

720 degrees / 360 degrees = 2

So, 720 degrees represents two times around the circle.

To find the positive degree measure that arrives at the same place on the unit circle as negative 90 degrees, we can consider that one complete revolution around the unit circle is 360 degrees. Therefore, adding 360 degrees to -90 degrees will bring us to the same place:

-90 degrees + 360 degrees = 270 degrees

Thus, positive 270 degrees arrives at the same place on the unit circle as negative 90 degrees.

Answer 2

1: 360. 2: 2 times. 3: 270 degrees.

Explanation:

Here's a picture for reference. A circle is split into 360 degrees, so going a full rotation would equate to 360 degrees. Following this logic we see that 720 degrees is just two rotations of a circle. Additionally, -90 degrees on a circular path would be equal to a rotation of positive 270.

Hope this Helps.