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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=((1)/(2),(sqrt3)/(2)) 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^{\circ} \leq \theta<360^{\circ} .\newlineP=(12,32) P=\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \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=(12,32) P=\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \newlineAnswer:
  1. Identify Coordinates: Identify the coordinates of point PP on the unit circle.\newlinePoint PP has coordinates (12,32)(\frac{1}{2}, \frac{\sqrt{3}}{2}). On the unit circle, these coordinates correspond to (cos⁡(θ),sin⁡(θ))(\cos(\theta), \sin(\theta)).
  2. Determine Quadrant: Determine the quadrant in which the angle θ\theta lies.\newlineSince both coordinates are positive, point PP lies in the first quadrant. Angles in the first quadrant range from 00 to 9090 degrees.
  3. Find Angle: Use the known sine or cosine value to find the angle θ\theta. We can use the cosine value, which is 12\frac{1}{2}, to find the angle. The angle whose cosine is 12\frac{1}{2} is 6060 degrees.
  4. Verify Angle: Verify the angle using the sine value.\newlineThe sine value is 3/2\sqrt{3}/2, which also corresponds to an angle of 6060 degrees. This confirms that the angle θ\theta is indeed 6060 degrees.
  5. Adjust if Necessary: Determine if the angle needs to be adjusted to the nearest tenth of a degree.\newlineSince the angle is exactly 6060 degrees, there is no need for adjustment to the nearest tenth of a degree.

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