Find the Cartesian coordinates of a point on the unit circle at a given angle ( heta ).
Answer 1
Daniel Carter
First, recall that for any point on the unit circle, its coordinates can be represented as \((x, y) = (\cos \theta, \sin \theta)\).
Given an angle \(\theta = \frac{3\pi}{4}\), we can calculate the coordinates as follows:
$ x = \cos \left( \frac{3\pi}{4} \right) = \cos \left(135^\circ \right) = -\frac{\sqrt{2}}{2} $
$ y = \sin \left( \frac{3\pi}{4} \right) = \sin \left(135^\circ \right) = \frac{\sqrt{2}}{2} $
Therefore, the Cartesian coordinates of the point are \( \left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) \).
Answer 2
Christopher Garcia
To find the Cartesian coordinates for a given angle ( heta) on the unit circle, use the formulas (x = cos heta) and (y = sin heta).
For ( heta = frac{3pi}{4}), we calculate:
$ x = cos left( frac{3pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ y = sin left( frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $
Thus, the coordinates are ( left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) ).
Answer 3
John Anderson
The coordinates on the unit circle for ( heta = frac{3pi}{4}) are:
$ x = cos left( frac{3pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ y = sin left( frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $
The coordinates are ( left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) ).
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