Question

which angle has its terminal side on the positive y-axis?
a. π radians
b. \\(\frac{π}{4}\\) radians
c. 2π radians
d. \\(\frac{π}{2}\\) radians

Explanation:

Step1: Recall angle positions

In the unit circle, angles are measured from the positive x - axis. The positive y - axis corresponds to an angle of $\frac{\pi}{2}$ radians (or 90 degrees) when measured counter - clockwise from the positive x - axis. Let's analyze each option:

• Option A: $\pi$ radians is equivalent to 180 degrees, and its terminal side is on the negative x - axis.
• Option B: $\frac{\pi}{4}$ radians is equivalent to 45 degrees, and its terminal side is in the first quadrant, between the positive x - axis and positive y - axis.
• Option C: $2\pi$ radians is equivalent to 360 degrees, and its terminal side is on the positive x - axis (same as the initial side).
• Option D: $\frac{\pi}{2}$ radians (assuming the option is $\frac{\pi}{2}$ radians, maybe a typo in the original, but from the context of the question about positive y - axis angle) has a terminal side on the positive y - axis.

Step2: Match with the positive y - axis

We know that the angle with its terminal side on the positive y - axis (when measured counter - clockwise from the positive x - axis) is $\frac{\pi}{2}$ radians. Among the given options, the one that represents this angle is the option with $\frac{\pi}{2}$ radians (assuming option D is $\frac{\pi}{2}$ radians, likely a formatting issue in the original question).

Answer:

D. $\frac{\pi}{2}$ radians (assuming the option D is $\frac{\pi}{2}$ radians as it is the angle with terminal side on positive y - axis)