Question

The angle y formed at the center of the circle, with its initial ray at positive of the x axis, and its final ray is 1/9 of the complete rotation about the origin shown below. What is the measure of angle o, in degrees and in radians?

1) 60° and i - radians
2) 60° and 3 radians
3) 120° and i radians
4) 120° and 21 radians

Answer 1

The measure of angle y, which is 1/9 of a complete rotation, is 40° or (2/9)π radians. The provided answer choices do not match the correct answer.

Step-by-step explanation:

Measure of Angle Y in Degrees and Radians

To find the measure of angle y, which is 1/9 of a complete rotation, we first need to understand the full rotation measures.

One complete revolution, or 360 degrees, equals 2π radians. Since y is 1/9 of a complete rotation, we divide 360 degrees by 9 to find the degree measure, and 2π radians by 9 for the radian measure:

360°/9 = 40°
2π rad/9 = (2/9π) rad

Therefore, the measure of angle y is 40° or approximately (2/9)π radians. Note that none of the answer choices provided in the question seem to match the correct calculations.