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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=(-(sqrt2)/(2),-(sqrt2)/(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=(−22,−22) P=\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{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=(−22,−22) P=\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right) \newlineAnswer:
  1. Identify Quadrant: To find the angle θ\theta that corresponds to a point on the unit circle, we need to determine in which quadrant the point lies and use the reference angle associated with that point.\newlineThe given point P=(−(2)/(2),−(2)/(2))P=(-(\sqrt{2})/(2),-(\sqrt{2})/(2)) has both negative xx and yy coordinates, which places it in the third quadrant.
  2. Determine Reference Angle: In the unit circle, the reference angle is the acute angle that the terminal side makes with the x-axis. Since the point has equal absolute values for xx and yy, the reference angle is 4545 degrees or π/4\pi/4 radians.
  3. Calculate Actual Angle: To find the actual angle θ\theta, we need to add 180180 degrees to the reference angle because the angle is in the third quadrant. So, θ=180\theta = 180 degrees +45+ 45 degrees.
  4. Final Angle Calculation: Performing the addition, we get θ=225\theta = 225 degrees. This is the angle in degrees of the terminal side through the point PP on the unit circle.

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