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If the angle theta=-(3pi)/(4) is in standard position on the unit circle, what ordered pair does its terminal side pass through?

If the angle θ=−3π4 \theta=-\frac{3 \pi}{4} is in standard position on the unit circle, what ordered pair does its terminal side pass through?

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Q. If the angle θ=−3π4 \theta=-\frac{3 \pi}{4} is in standard position on the unit circle, what ordered pair does its terminal side pass through?
  1. Position on Unit Circle: Understand the position of the angle on the unit circle. The angle θ=−3π4\theta=-\frac{3\pi}{4} is in the third quadrant of the unit circle because it is negative and its absolute value is greater than π2\frac{\pi}{2} but less than π\pi.
  2. Reference Angle Determination: Determine the reference angle for θ=−3π4\theta=-\frac{3\pi}{4}.\newlineThe reference angle is the acute angle that the terminal side of θ\theta makes with the x-axis. Since θ\theta is in the third quadrant, its reference angle is π−∣θ∣=π−3π4=π4\pi - |\theta| = \pi - \frac{3\pi}{4} = \frac{\pi}{4}.
  3. Coordinates for Reference Angle: Find the coordinates for the reference angle π/4\pi/4 on the unit circle.\newlineFor the reference angle π/4\pi/4, the coordinates on the unit circle are (2/2,2/2)(\sqrt{2}/2, \sqrt{2}/2) because the unit circle has a radius of 11, and these are the xx and yy values for that angle in the first quadrant.
  4. Adjusting Coordinates: Adjust the coordinates for the third quadrant.\newlineSince θ=−3π4\theta=-\frac{3\pi}{4} is in the third quadrant, both the xx and yy coordinates will be negative. Therefore, the coordinates for θ=−3π4\theta=-\frac{3\pi}{4} are (−2/2,−2/2)(-\sqrt{2}/2, -\sqrt{2}/2).

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