If the initial side of an angle in standard position lies along the positive $x$-axis and is rotated clockwise to coincide with the negative $y$-axis, by what angle (in $\mathrm{degrees}$) has it turned?

• A. $90$ degrees
• B. $360$ degrees
• C. $180$ degrees
• D. $270$ degrees

Answer: (D)

Verified step by step guidance

1. Understand that the initial side of the angle lies along the positive x-axis, which corresponds to 0 degrees in standard position.
2. Recognize that rotating clockwise means the angle measure will be negative if measured in the usual positive (counterclockwise) direction, but the problem asks for the positive equivalent angle measure.
3. Identify the final position of the terminal side of the angle, which is along the negative y-axis. In standard position, the negative y-axis corresponds to 270 degrees when measured counterclockwise from the positive x-axis.
4. Since the rotation is clockwise, the angle can be thought of as a negative rotation of 90 degrees, but to express it as a positive angle between 0 and 360 degrees, add 360 degrees to -90 degrees, resulting in 270 degrees.
5. Conclude that the angle turned clockwise from the positive x-axis to the negative y-axis is 270 degrees.