On the unit circle, find the coordinates of the point corresponding to the angle $frac{5pi}{4}$ radians.
Answer 1
Joseph Robinson
To find the coordinates of the point corresponding to the angle $\frac{5\pi}{4}$ radians on the unit circle, we utilize the unit circle’s properties.
First, note that $\frac{5\pi}{4}$ radians is in the third quadrant, where both sine and cosine values are negative.
The reference angle for $\frac{5\pi}{4}$ radians is $\pi – \frac{\pi}{4} = \frac{\pi}{4}$ radians.
For $\frac{\pi}{4}$ radians, the coordinates are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.
In the third quadrant, both coordinates are negative, so the coordinates for $\frac{5\pi}{4}$ radians are:
$\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$
Answer 2
Alex Thompson
We start by noting the angle $frac{5pi}{4}$ radians on the unit circle. This angle places us in the third quadrant.
In the third quadrant, both sine and cosine are negative.
The reference angle for $frac{5pi}{4}$ is $frac{pi}{4}$ radians, whose coordinates on the unit circle are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.
Adjusting for the third quadrant, we get:
$left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$
Answer 3
Abigail Nelson
Given the angle $frac{5pi}{4}$ radians on the unit circle, we determine:
Coordinates in the third quadrant are negative, so:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $
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