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

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

Answer: (D)

Verified step by step guidance

1. Identify that the point (0, 1) lies on the unit circle, which means it satisfies the equation \(x^2 + y^2 = 1\).
2. Recall that the angle \(t\) in standard position has its terminal side passing through the point on the unit circle, so the coordinates of the point correspond to \((\cos t, \sin t)\).
3. Since the point is (0, 1), set \(\cos t = 0\) and \(\sin t = 1\).
4. Determine the angle \(t\) whose cosine is 0 and sine is 1. This corresponds to the angle where the terminal side points straight up on the unit circle.
5. Recall that this angle in degrees is \(90^\circ\), which is the measure of angle \(t\).