Question

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

Answer 1

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

Answer 2

Answer:

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

Step-by-step 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

$\frac{23 \pi}{3} -\frac{6 \pi}{3} =\frac{17 \pi}{3} \quad \frac{17 \pi}{3} -\frac{6 \pi}{3} =\frac{11 \pi}{3}\quad \frac{11 \pi}{3} -\frac{6 \pi}{3} =\frac{5 \pi}{3}$

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

Answer F is another valid answer since

$-\frac{7 \pi}{3} +\frac{6 \pi}{3} =-\frac{\pi}{3}$