Is 300 an angle between 0 and 360 degrees that is coterminal with -780 degrees?

-780 + 360 = -420 once around

-420 + 360 = -60 twice around

-60 + 360 = 300 sure enough

To determine if 300 degrees is an angle between 0 and 360 degrees that is coterminal with -780 degrees, we need to check if they have the same reference angle.

First, let's find the reference angle for both -780 degrees and 300 degrees:

For -780 degrees:
Since -780 degrees is negative, we can add 360 degrees repeatedly until we get a positive angle less than 360 degrees.
-780 + 360 = -420 (still negative)
-420 + 360 = -60 (still negative)
-60 + 360 = 300 (positive)

So, the reference angle for -780 degrees is 300 degrees.

For 300 degrees:
Since 300 degrees is already positive and less than 360 degrees, its reference angle is 300 degrees.

Now, comparing the reference angles, we can see that both -780 degrees and 300 degrees have the same reference angle of 300 degrees.

Therefore, 300 degrees is an angle between 0 and 360 degrees that is coterminal with -780 degrees.

To determine if 300 degrees is an angle between 0 and 360 degrees that is coterminal with -780 degrees, we need to check if 300 degrees lies within the range of 0 to 360 degrees and if it is equivalent to -780 degrees when adjusted by multiples of 360 degrees.

First, let's check if 300 degrees is within the range of 0 to 360 degrees. Since both 0 and 360 degrees are inclusive in this range, we can say that 300 degrees falls within the range.

To determine if 300 degrees is coterminal with -780 degrees, we need to compare their values after accounting for multiples of 360 degrees.

We can start by finding an equivalent angle for -780 degrees within the range of 0 to 360 degrees. To do this, we can repeatedly add or subtract 360 degrees until we get within that range.

-780 degrees + 360 degrees = -420 degrees
-420 degrees + 360 degrees = -60 degrees
-60 degrees + 360 degrees = 300 degrees

As you can see, after adjusting for multiples of 360 degrees, -780 degrees is equivalent to 300 degrees. This makes 300 degrees and -780 degrees coterminal angles.

Therefore, yes, 300 degrees is an angle between 0 and 360 degrees that is coterminal with -780 degrees.