Determine the coordinates of the point on the unit circle corresponding to the angle $frac{7pi}{6}$ radians.
Answer 1
Sophia Williams
To find the coordinates of the point on the unit circle corresponding to the angle $\frac{7\pi}{6}$ radians, we need to consider the angle in standard position.
The angle $\frac{7\pi}{6}$ radians is in the third quadrant, where both sine and cosine are negative.
The reference angle is $\frac{\pi}{6}$ radians.
The coordinates for $\frac{\pi}{6}$ radians on the unit circle are $(\frac{\sqrt{3}}{2}, \frac{1}{2})$.
Since $\frac{7\pi}{6}$ is in the third quadrant, the coordinates are:
$\left( -\frac{\sqrt{3}}{2}, -\frac{1}{2} \right)$
Answer 2
Abigail Nelson
First, convert $frac{7pi}{6}$ radians to degrees: $frac{7pi}{6} imes frac{180}{pi} = 210^circ$.
210 degrees is in the third quadrant, where both x and y coordinates are negative.
The reference angle for 210 degrees is $210^circ – 180^circ = 30^circ$.
We know the coordinates for $30^circ$ on the unit circle are $(frac{sqrt{3}}{2}, frac{1}{2})$.
Thus, for $210^circ$ (or $frac{7pi}{6}$ radians), the coordinates are:
$left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight)$
Answer 3
Thomas Walker
Given $frac{7pi}{6}$ radians:
– Reference angle is $frac{pi}{6}$
– Quadrant: 3rd (both coordinates are negative)
Coordinates:
$left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight)$
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