Question

Select all angles that are coterminal with an angle of rotation of 300 degrees

A. -420 degrees

B. 2100 degrees

C. -900 degrees

D. -π/3

E. 23π/3

F. -7π/3

Answer 1

The answers would be A,B,D, and F!

Answer 2

A. B. D. E. F. are all coterminal angles to 300°.

Explanation:

A 360 degree angle is a complete turn of a circle, if you keep going you can reset the counter or keep it and it will still be valid, therefore a 361° angle is the same as a 1° angle. With that in mind you can keep substracting 360 to answer B. to check if it is valid:

`2100-360=1740\quad 1740-360=1380\quad 1380-360=1020\quad 1020-360=660\quad 660-360=300`

so answer B. gives the same angle (coterminal) to 300°.

In case of a negative angle you sweep the angle clockwise, instead of the normal positive counterclockwise. In that order of ideas, a -1° angle is the same a 359°. So you can add 360° to see if it reaches the desired angle.

In case of angle A.

`-420+360=-60\quad -60+360=300`

It is valid. Let's look at angle C.

`-900+360=-540\quad -540+360=-180\quad -180+360=180`

It is not coterminal with 300°.

To the angles in radians, remember that a pi/3 angle is just a 60° angle. Thus, answer D. is valid because a -60° is coterminal with a 300° angle.

Answer E. is examined taking into account that a 360° angle is just a 2 pi angle, or a 6 pi/3 angle. So

`(23 \pi)/(3) -(6 \pi)/(3) =(17 \pi)/(3) \quad (17 \pi)/(3) -(6 \pi)/(3) =(11 \pi)/(3)\quad  (11 \pi)/(3) -(6 \pi)/(3) =(5 \pi)/(3)`

Which is exactly a 300° angle (check the image attached, look for the blue lines).

Answer F is another valid answer since

`-(7 \pi)/(3) +(6 \pi)/(3) =-(\pi)/(3)`