Along with the image below, Use your knowledge of the unit circle and radian measure of angles to answer the following questions

Question

a. Consider circles 1 through 6. If these circles are equally spaced around the main circle, and circle 1 is at 0°, what is the direction (in degrees) of each of these circles in relation to the main circle?

b. Consider circles 7 through 12. If circle 7 is at 45°, what is the radian measure of each of these circles in relation to the main circle? Explain how you know these values.

c. If the center of circle 3 is 100 feet away from the main circle, what are the coordinates of the center of circle 3 (the origin is at the center of the main circle)? Use these coordinates to prove that the distance from the centers of circle 3 and the main circle are 100 feet apart.

d. After creating the design, the designers want to inspect their work. They start at 0° and walk all the way around the design almost two times and stop at circle 12. How many radians did they cover during their inspection?

e. Consider circles 5 and 6. In relation to the main circles, do the center points of circles 5 and 6 have even or odd symmetry? Why?

Answer 1

Consider that the unit circle has 2π radians and there fore 6 arms, how far apart are they?