If an angle $r$ in standard position has its terminal side passing through the point $(0,1)$ on the unit circle, what is the measure of angle $r$ in degrees?

• A. $0°$
• B. $270°$
• C. $90°$
• D. $180°$

Answer: (C)

Verified step by step guidance

1. Recall that points on the unit circle have coordinates of the form \((\cos r, \sin r)\), where \(r\) is the angle in standard position measured from the positive x-axis.
2. Given the point \((0, 1)\) lies on the terminal side of angle \(r\), identify the cosine and sine values: \(\cos r = 0\) and \(\sin r = 1\).
3. Use the sine and cosine values to determine the angle \(r\). Since \(\cos r = 0\) and \(\sin r = 1\), this corresponds to an angle where the terminal side points straight up on the unit circle.
4. Recall the common angles on the unit circle: \$90^\circ\( (or \)\frac{\pi}{2}\( radians) has coordinates \)(0, 1)$, which matches the given point.
5. Conclude that the measure of angle \(r\) in degrees is \$90^\circ$.