Find the coordinates of the point where the terminal side of the angle intersects the unit circle at an angle of $frac{5pi}{4}$ radians
Answer 1
Emma Johnson
To find the coordinates of the point where the terminal side of the angle intersects the unit circle at an angle of $\frac{5\pi}{4}$ radians, we use the unit circle properties.
The angle $\frac{5\pi}{4}$ radians is in the third quadrant where both sine and cosine values are negative.
The reference angle for $\frac{5\pi}{4}$ is $\frac{\pi}{4}$.
The coordinates on the unit circle for an angle of $\frac{\pi}{4}$ are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.
Since we are in the third quadrant, we change the signs of both x and y coordinates:
Therefore, the coordinates are:
$ \left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right) $
Answer 2
Joseph Robinson
To find the coordinates at $frac{5pi}{4}$ radians:
The reference angle is $frac{pi}{4}$, with standard coordinates $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Since the angle is in the third quadrant, both values are negative:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $
Answer 3
Samuel Scott
Use unit circle properties for $frac{5pi}{4}$:
Coordinates in third quadrant:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $
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