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For the rotation 1388 degrees, find the coterminal angle from 0 degrees, where 0 degrees ≤ θ < 360 degrees. Also, determine the quadrant and the reference angle.

User InVader
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Final answer:

The coterminal angle from 0 degrees for a rotation of 1388 degrees is 88 degrees in the fourth quadrant. The reference angle is also 88 degrees.

Step-by-step explanation:

To find the coterminal angle from 0 degrees for a rotation of 1388 degrees, we need to determine how many complete revolutions it represents. Since one complete revolution is 360 degrees, we divide 1388 degrees by 360 to get a quotient of 3 and a remainder of 88. So, the coterminal angle from 0 degrees is 88 degrees.

In terms of quadrant, we can determine it by looking at the sign of the angle. Since the angle is positive, it lies in the fourth quadrant. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. In this case, the reference angle is 88 degrees.

User Reinaldo Junior
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