Find the coordinates of a point on the flipped unit circle at a given angle
Answer 1
Abigail Nelson
Given the angle $\theta = \frac{\pi}{3}$, find the coordinates of the corresponding point on the flipped unit circle where the x and y coordinates are switched.
The standard coordinates for $\theta = \frac{\pi}{3}$ on the unit circle are $(cos(\frac{\pi}{3}), sin(\frac{\pi}{3})) = (\frac{1}{2}, \frac{\sqrt{3}}{2})$.
For the flipped unit circle, the coordinates are switched, giving us $(y, x)$.
Therefore, the coordinates of the point at $\theta = \frac{\pi}{3}$ on the flipped unit circle are $(\frac{\sqrt{3}}{2}, \frac{1}{2}).$
Answer 2
Ava Martin
Given the angle $ heta = frac{pi}{4}$, determine the coordinates of the point on the flipped unit circle where the x and y coordinates are interchanged.
On the standard unit circle, the coordinates for $ heta = frac{pi}{4}$ are $(cos(frac{pi}{4}), sin(frac{pi}{4})) = (frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.
Switching the coordinates for the flipped unit circle, we get $(y, x)$.
Thus, the coordinates of the point at $ heta = frac{pi}{4}$ on the flipped unit circle are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}).$
Answer 3
Mia Harris
Given the angle $ heta = frac{pi}{6}$, find the point’s coordinates on the flipped unit circle.
For $ heta = frac{pi}{6}$, the standard unit circle coordinates are $(cos(frac{pi}{6}), sin(frac{pi}{6})) = (frac{sqrt{3}}{2}, frac{1}{2})$.
Swapping x and y for the flipped unit circle gives us $(frac{1}{2}, frac{sqrt{3}}{2}).$
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