Determine the sine and cosine of an angle in a unit circle
Answer 1
Samuel Scott
Given an angle of $\frac{\pi}{4}$ radians, determine the coordinates on the unit circle.
In a unit circle, the coordinates for $\frac{\pi}{4}$ are $(\cos(\frac{\pi}{4}), \sin(\frac{\pi}{4}))$.
Using the known values:
$\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
$\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
Therefore, the coordinates are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.
Answer 2
William King
Given an angle of $frac{pi}{6}$ radians, determine the coordinates on the unit circle.
In a unit circle, the coordinates for $frac{pi}{6}$ are $(cos(frac{pi}{6}), sin(frac{pi}{6}))$.
Using the known values:
$cos(frac{pi}{6}) = frac{sqrt{3}}{2} $
$sin(frac{pi}{6}) = frac{1}{2} $
Therefore, the coordinates are $(frac{sqrt{3}}{2}, frac{1}{2})$.
Answer 3
Lucas Brown
Given an angle of $frac{pi}{3}$ radians, determine the coordinates on the unit circle.
In a unit circle, the coordinates for $frac{pi}{3}$ are $(cos(frac{pi}{3}), sin(frac{pi}{3}))$.
Using the known values:
$cos(frac{pi}{3}) = frac{1}{2} $
$sin(frac{pi}{3}) = frac{sqrt{3}}{2} $
Therefore, the coordinates are $(frac{1}{2}, frac{sqrt{3}}{2})$.
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