Are the angles 117 in degrees and 477 in degrees coterminal?

Yes, they are coterminal.

Step-by-step 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°.

You are given 117°.

To find angles that are coterminal with 117°, we do the following:

117° + 360° = 477°

117° - 360° = 243°

As you can see, when we added 117° to 360°, we got 477°.

To answer your question, YES.

You now know that 117° and 477° are coterminal angles.

Keep in mind that 477° is not the only coterminal angle to 117°.

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