Find the coordinates of the point on the unit circle that corresponds to an angle of $frac{7pi}{6}$ radians.
Answer 1
Charlotte Davis
To find the coordinates of the point on the unit circle that corresponds to an angle of $\frac{7\pi}{6}$ radians, we can use the unit circle definitions.
The angle $\frac{7\pi}{6}$ radians is in the third quadrant where both x and y coordinates are negative.
First, we need to find the reference angle, which is $\pi – \frac{7\pi}{6} = \frac{\pi}{6}$ radians.
The coordinates corresponding to the reference angle $\frac{\pi}{6}$ are $(\frac{\sqrt{3}}{2}, \frac{1}{2})$.
Since $\frac{7\pi}{6}$ is in the third quadrant, both coordinates will be negative. Thus, the coordinates at $\frac{7\pi}{6}$ will be:
$\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$
Answer 2
Daniel Carter
To determine the coordinates of the point on the unit circle for $frac{7pi}{6}$ radians, remember that the unit circle has a radius of 1.
Since $frac{7pi}{6}$ is in the third quadrant, the coordinates will be negative.
Calculate the reference angle: $pi – frac{7pi}{6} = frac{pi}{6}$ radians.
The coordinates for $frac{pi}{6}$ are $left(frac{sqrt{3}}{2}, frac{1}{2}
ight)$.
Converting these to the third quadrant:
$left(-frac{sqrt{3}}{2}, -frac{1}{2}
ight)$
Answer 3
Lily Perez
For the angle $frac{7pi}{6}$ radians:
It lies in the third quadrant.
The reference angle is $frac{pi}{6}$ radians.
Coordinates for $frac{pi}{6}$ are $left(frac{sqrt{3}}{2}, frac{1}{2}
ight)$.
So, coordinates are:
$left(-frac{sqrt{3}}{2}, -frac{1}{2}
ight)$
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