If angle $BAC$ is in standard position and its terminal side passes through the point $(0,1)$ on the unit circle, what is the measure of angle $BAC$ in degrees?

• A. $30°$
• B. $60°$
• C. $90°$
• D. $45°$

Answer: (C)

Verified step by step guidance

1. Identify that the angle \( \angle BAC \) is in standard position, meaning its vertex is at the origin and its initial side lies along the positive x-axis.
2. Recognize that the terminal side of the angle passes through the point \( (0, 1) \) on the unit circle, which means the radius vector from the origin to this point defines the angle.
3. Recall that points on the unit circle have coordinates \( (\cos \theta, \sin \theta) \), where \( \theta \) is the angle in standard position.
4. Since the point is \( (0, 1) \), set \( \cos \theta = 0 \) and \( \sin \theta = 1 \), and determine the angle \( \theta \) that satisfies these conditions.
5. Use your knowledge of special angles on the unit circle to conclude that the angle with \( \cos \theta = 0 \) and \( \sin \theta = 1 \) corresponds to \( \theta = 90^\circ \).