Find the coordinates of the point on the unit circle where the angle in radians is $frac{7pi}{6}$.
Answer 1
Daniel Carter
To find the coordinates of the point on the unit circle at the angle $\frac{7\pi}{6}$, we use the cosine and sine functions.
1. The angle $\frac{7\pi}{6}$ is in the third quadrant where both cosine and sine are negative.
2. The reference angle for $\frac{7\pi}{6}$ is $\frac{\pi}{6}$.
3. The cosine and sine of $\frac{\pi}{6}$ are $\frac{\sqrt{3}}{2}$ and $\frac{1}{2}$, respectively.
4. Therefore, the coordinates are:
$ \left( -\frac{\sqrt{3}}{2}, -\frac{1}{2} \right) $
Answer 2
Emma Johnson
Let’s determine the coordinates of the point on the unit circle at $frac{7pi}{6}$.
1. $frac{7pi}{6}$ places the terminal side in the third quadrant.
2. The reference angle is $frac{pi}{6}$, with cosine and sine values of $frac{sqrt{3}}{2}$ and $frac{1}{2}$.
3. In the third quadrant, both cosine and sine are negative, so the coordinates are:
$ left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight) $
Answer 3
Samuel Scott
1. Angle $frac{7pi}{6}$ is in the third quadrant with negative cosine and sine.
2. Reference angle $frac{pi}{6}$ has values $frac{sqrt{3}}{2}$ and $frac{1}{2}$.
3. Coordinates:
$ left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight) $
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