Answer:
Yes, they are coterminal.
Explanation:
Coterminal angles are angles that are in multiples of -360 degrees or +360 degrees away from the initial angle.
Therefore, the easiest way to check if an angle is coterminal is set up an equation.

We get a true statement, which means that 117 is a coterminal angle of 477 and 477 is a coterminal angle of 117.
We can also determine the value in radians.

117° in radians is
. Coterminal angles for radians are multiples of
, either negative or positive.
However, we also need to determine the value of 477 in radians too.

So, if we add
to
:

Therefore, even in radians, 477° is an angle coterminal to 117°.