Find the coordinates on the unit circle for an angle of $135^{circ}$
Answer 1
Michael Moore
To find the coordinates on the unit circle for an angle of $135^{\circ}$, we first convert degrees to radians.
$135^{\circ} = \frac{135 \pi}{180} = \frac{3\pi}{4}$
Next, we use the unit circle definitions for sine and cosine at $\frac{3 \pi}{4}$.
$\cos \left( \frac{3\pi}{4} \right) = -\frac{\sqrt{2}}{2}$
$\sin \left( \frac{3\pi}{4} \right) = \frac{\sqrt{2}}{2}$
Thus, the coordinates are:
$\left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$
Answer 2
Sophia Williams
To determine the coordinates at $135^{circ}$ on the unit circle, we start by converting the angle to radians:
$135^{circ} = frac{135 pi}{180} = frac{3pi}{4}$
Using the unit circle, we know:
$cos left( frac{3pi}{4}
ight) = -frac{sqrt{2}}{2}$
$sin left( frac{3pi}{4}
ight) = frac{sqrt{2}}{2}$
Therefore, the resulting coordinates are:
$left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$
Answer 3
John Anderson
Convert $135^{circ}$ to radians:
$frac{135 pi}{180} = frac{3pi}{4}$
Find the cosine and sine:
$cos left( frac{3pi}{4}
ight) = -frac{sqrt{2}}{2}$
$sin left( frac{3pi}{4}
ight) = frac{sqrt{2}}{2}$
Coordinates:
$left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$
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