Determine the coordinates of ( frac{3pi}{4} ) on the unit circle
Answer 1
Joseph Robinson
The angle \( \frac{3\pi}{4} \) is in the second quadrant of the unit circle. To find its coordinates, we start by noting that the reference angle for \( \frac{3\pi}{4} \) is \( \frac{\pi}{4} \). The coordinates for \( \frac{\pi}{4} \) are \( \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) \).
Since \( \frac{3\pi}{4} \) is in the second quadrant, the x-coordinate will be negative, and the y-coordinate will be positive. Therefore:
$ \text{Coordinates of } \frac{3\pi}{4} = \left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $
Answer 2
Maria Rodriguez
We need to find the coordinates of the angle ( frac{3pi}{4} ) on the unit circle. The reference angle for ( frac{3pi}{4} ) is ( frac{pi}{4} ), which has coordinates ( left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) ).
Since ( frac{3pi}{4} ) lies in the second quadrant, we flip the sign of the x-coordinate:
$ ext{Coordinates of } frac{3pi}{4} = left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
Answer 3
Amelia Mitchell
The reference angle for ( frac{3pi}{4} ) is ( frac{pi}{4} ). In the second quadrant, this translates to coordinates:
$ left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
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