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

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

Answer: (A)

Verified step by step guidance

1. Recall that an angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side is the ray that rotates from the initial side to the angle's measure.
2. Since the point (0, 1) lies on the unit circle, it corresponds to a point where the radius vector from the origin makes a certain angle with the positive x-axis. The unit circle equation is \(x^2 + y^2 = 1\), and the point (0, 1) satisfies this.
3. On the unit circle, the coordinates of a point are given by \((\cos c, \sin c)\), where \(c\) is the angle in standard position. Here, \(\cos c = 0\) and \(\sin c = 1\).
4. Identify the angle \(c\) whose cosine is 0 and sine is 1. This corresponds to the angle where the terminal side points straight up along the positive y-axis.
5. Recall the common angles on the unit circle and their sine and cosine values. The angle with \(\cos c = 0\) and \(\sin c = 1\) is \$90^\circ$.