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Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0^(@) <= theta < 360^(@). P=(0,1) Answer:

Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlineP=(0,1) P=(0,1) \newlineAnswer:

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Q. Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlineP=(0,1) P=(0,1) \newlineAnswer:
  1. Determine Position Angle θ\theta: Determine the standard position of the angle θ\theta whose terminal side passes through the point P=(0,1)P=(0,1) on the unit circle. The point (0,1)(0,1) corresponds to the top of the unit circle where the y-coordinate is 11 and the x-coordinate is 00. This is the point where the unit circle intersects the positive y-axis.
  2. Recall Angle Measurement: Recall that the angle in standard position whose terminal side intersects the positive y-axis is 9090 degrees or π2\frac{\pi}{2} radians. This is because the angle is measured from the positive x-axis, and a quarter turn counter-clockwise (which is the positive direction for angles) places the terminal side on the positive y-axis.
  3. Exact Angle Calculation: Since the point (0,1)(0,1) is exactly at the top of the unit circle, we do not need to approximate the angle; it is exactly 9090 degrees. There is no need for further calculation or approximation to the nearest tenth of a degree.

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