An angle in standard position measures \( \frac{\pi}{2} \) radians, and \( P(0,1) \) is on the terminal side of the angle. What is the value of the cosine of this angle? -1 1 undefined

To find the cosine of the angle measuring \( \frac{\pi}{2} \) radians, we can analyze the position of the point \( P(0,1) \) on the terminal side of the angle. 1. **Understanding the angle**: An angle of \( \frac{\pi}{2} \) radians corresponds to 90 degrees. In standard position, this angle starts from the positive x-axis and rotates counterclockwise to the positive y-axis. 2. **Identifying the coordinates**: The point \( P(0,1) \) lies on the positive y-axis, which is indeed the terminal side of the angle \( \frac{\pi}{2} \). 3. **Calculating cosine**: The cosine of an angle in the unit circle is defined as the x-coordinate of the point on the terminal side of the angle. For the point \( P(0,1) \): - The x-coordinate is \( 0 \). Thus, the cosine of the angle \( \frac{\pi}{2} \) radians is: \[ \cos\left(\frac{\pi}{2}\right) = 0 \] Since the options provided are -1, 1, and undefined, the correct answer is not listed. However, the cosine of \( \frac{\pi}{2} \) is indeed \( 0 \).