Determine the coordinates of the point on the unit circle corresponding to an angle of $frac{5pi}{4}$ radians.
Answer 1
Lucas Brown
To find the coordinates of the point on the unit circle corresponding to an angle of $\frac{5\pi}{4}$ radians, we can use the unit circle properties.
The angle $\frac{5\pi}{4}$ is located in the third quadrant of the unit circle. The reference angle for $\frac{5\pi}{4}$ is $\pi – \frac{5\pi}{4} = \frac{\pi}{4}$, which corresponds to a 45-degree angle.
For a point in the third quadrant, both the sine (y-coordinate) and cosine (x-coordinate) values will be negative. The coordinates of a 45-degree angle on the unit circle are (sqrt(2)/2, sqrt(2)/2). Therefore, the coordinates for the angle $\frac{5\pi}{4}$ will be:
$\left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right)$
Answer 2
Mia Harris
To determine the coordinates of the point corresponding to the angle $frac{5pi}{4}$ radians:
1. Recognize that $frac{5pi}{4}$ is in the third quadrant.
2. Calculate the reference angle: $pi + frac{pi}{4} = frac{5pi}{4}$
3. The coordinates for $frac{pi}{4}$ are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$ on the unit circle.
Since $frac{5pi}{4}$ is in the third quadrant, both coordinates are negative:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$
Answer 3
Chloe Evans
For the angle $frac{5pi}{4}$ on the unit circle:
1. Recognize the angle is in the third quadrant.
2. Reference angle is $frac{pi}{4}$ with coordinates (sqrt(2)/2, sqrt(2)/2).
3. Convert to third quadrant values:
$ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$
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