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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=((sqrt3)/(2),-(1)/(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=(32,−12) P=\left(\frac{\sqrt{3}}{2},-\frac{1}{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=(32,−12) P=\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \newlineAnswer:
  1. Identify Coordinates: Identify the coordinates of the point on the unit circle.\newlineThe given point PP has coordinates (32,−12)\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right). These coordinates correspond to (cos⁡(θ),sin⁡(θ))(\cos(\theta), \sin(\theta)) on the unit circle.
  2. Determine Reference Angle: Determine the reference angle.\newlineThe reference angle is the acute angle that the terminal side of θ\theta makes with the x-axis. Since the x-coordinate is positive and the y-coordinate is negative, the point lies in the fourth quadrant. The reference angle can be found using the cosine value, which is 3/2\sqrt{3}/2. The reference angle whose cosine is 3/2\sqrt{3}/2 is 3030 degrees or π/6\pi/6 radians.
  3. Find Actual Angle: Find the actual angle θ\theta. Since the point is in the fourth quadrant, we subtract the reference angle from 360360 degrees to find θ\theta. So, θ=360\theta = 360 degrees −30- 30 degrees =330= 330 degrees.

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