$ ext{Find the Coordinates of a Point on the Unit Circle}$
Answer 1
William King
Given a unit circle, find the coordinates of the point where the terminal side of an angle $\theta = \frac{5\pi}{4}$ intersects the circle.
Solution:
To find the coordinates of the point where the terminal side of an angle $\theta = \frac{5\pi}{4}$ intersects the unit circle, we use the following formulas:
$x = \cos(\theta)$
$y = \sin(\theta)$
For $\theta = \frac{5\pi}{4}$:
$x = \cos\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$
$y = \sin\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$
Therefore, the coordinates of the point are $\left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right)$.
Answer 2
Amelia Mitchell
Given a unit circle, find the coordinates of the point where the terminal side of an angle $ heta = 225^{circ}$ intersects the circle.
Solution:
To find the coordinates of the point where the terminal side of an angle $ heta = 225^{circ}$ intersects the unit circle, we use the following formulas:
$x = cos( heta)$
$y = sin( heta)$
For $ heta = 225^{circ}$ (which is equivalent to $frac{5pi}{4}$ radians):
$x = cos(225^{circ}) = -frac{sqrt{2}}{2}$
$y = sin(225^{circ}) = -frac{sqrt{2}}{2}$
Therefore, the coordinates of the point are $left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$.
Answer 3
Abigail Nelson
Given a unit circle, find the coordinates of the point where the terminal side of an angle $ heta = 225^{circ}$ intersects the circle.
Solution:
$x = cos(225^{circ}) = -frac{sqrt{2}}{2}$
$y = sin(225^{circ}) = -frac{sqrt{2}}{2}$
Therefore, the coordinates are $left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$.
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