$ ext{Find the Sine and Cosine of an Angle Given in a Flipped Unit Circle Problem}$
Answer 1
Samuel Scott
Given an angle $\theta$ in the flipped unit circle, where the x-values represent the sine of the angle and the y-values represent the cosine of the angle, find the sine and cosine of $\theta = \frac{5\pi}{4}$.
First, note that $\theta = \frac{5\pi}{4}$ is in the third quadrant. In the standard unit circle, $\sin(\frac{5\pi}{4}) = -\frac{1}{\sqrt{2}}$ and $\cos(\frac{5\pi}{4}) = -\frac{1}{\sqrt{2}}$.
Since the roles of sine and cosine are flipped, the sine of $\theta$ will be the x-coordinate, and the cosine of $\theta$ will be the y-coordinate.
Hence, the sine of $\theta = \frac{5\pi}{4}$ is $-\frac{1}{\sqrt{2}}$, and the cosine of $\theta = \frac{5\pi}{4}$ is $-\frac{1}{\sqrt{2}}$.
Answer 2
William King
Given an angle $ heta$ in the flipped unit circle, where the x-values represent the sine of the angle and the y-values represent the cosine of the angle, find the sine and cosine of $ heta = frac{3pi}{2}$.
First, note that $ heta = frac{3pi}{2}$ is in the fourth quadrant. In the standard unit circle, $sin(frac{3pi}{2}) = -1$ and $cos(frac{3pi}{2}) = 0$.
Since the roles of sine and cosine are flipped, the sine of $ heta$ will be the x-coordinate, and the cosine of $ heta$ will be the y-coordinate.
Hence, the sine of $ heta = frac{3pi}{2}$ is $-1$, and the cosine of $ heta = 0$.
Answer 3
Thomas Walker
Given an angle $ heta$ in the flipped unit circle, find the sine and cosine of $ heta = frac{2pi}{3}$.
In the standard unit circle, $sin(frac{2pi}{3}) = frac{sqrt{3}}{2}$ and $cos(frac{2pi}{3}) = -frac{1}{2}$.
Hence, the sine of $ heta = frac{2pi}{3}$ is $frac{sqrt{3}}{2}$, and the cosine of $ heta = -frac{1}{2}$.
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