Find the coordinates of the point on the unit circle where the angle is $frac{5pi}{4}$ radians.
Answer 1
Samuel Scott
To find the coordinates of the point on the unit circle where the angle is $ \frac{5\pi}{4} $ radians, we can use the definitions of sine and cosine for the unit circle.
The angle $ \frac{5\pi}{4} $ is in the third quadrant, where both sine and cosine are negative.
For the unit circle, the coordinates are given by $(\cos \theta, \sin \theta)$.
Thus, we find:
$ \cos \left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $
$ \sin \left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $
Therefore, the coordinates are:
$ \left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right) $
Answer 2
William King
To determine the coordinates for the angle $ frac{5pi}{4} $ on the unit circle, recall that in the third quadrant, both the sine and cosine values are negative.
We know that the coordinates on the unit circle can be written as $(cos heta, sin heta)$.
The cosine and sine values for $ frac{5pi}{4} $ radians are:
$ cos left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ sin left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
Hence, the coordinates are:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $
Answer 3
Christopher Garcia
The coordinates for the angle $ frac{5pi}{4} $ on the unit circle are found by recognizing that in the third quadrant, both sine and cosine are negative.
$ cos left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ sin left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
Therefore, the coordinates are:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $
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