Determine the coordinates of a point on the unit circle where the $sin( heta) = frac{1}{2}$ and the $ an( heta)$ value is positive.
Answer 1
Charlotte Davis
To find the coordinates where $\sin(\theta) = \frac{1}{2}$ and $\tan(\theta)$ is positive, we analyze the unit circle.
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The sine function equals $\frac{1}{2}$ at two angles: $\theta = \frac{\pi}{6}$ and $\theta = \frac{5\pi}{6}$.
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Since the tangent function is positive when both sine and cosine have the same sign, we consider the angles in the first and third quadrants.
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For $\theta = \frac{\pi}{6}$, the coordinates on the unit circle are:
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$ (\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6})) = (\frac{\sqrt{3}}{2}, \frac{1}{2}) $
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Thus, the coordinates are:
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$ (\frac{\sqrt{3}}{2}, \frac{1}{2}) $
Answer 2
Daniel Carter
For $sin( heta) = frac{1}{2}$ and a positive $ an( heta)$, we consider:
The angles $ heta = frac{pi}{6}$ and $ heta = frac{5pi}{6}$, but only $ heta = frac{pi}{6}$ has positive tangent.
The coordinates are:
$ (cos(frac{pi}{6}), sin(frac{pi}{6})) = (frac{sqrt{3}}{2}, frac{1}{2}) $
Answer 3
Chloe Evans
With $sin( heta) = frac{1}{2}$ and positive $ an( heta)$,
At $ heta = frac{pi}{6}$,
$ (frac{sqrt{3}}{2}, frac{1}{2}) $
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