Find the sine and cosine of angles using the unit circle
Answer 1
Chloe Evans
To find the sine and cosine of the angle $\theta = \frac{5\pi}{6}$ using the unit circle:
1. Locate the angle $\theta = \frac{5\pi}{6}$ on the unit circle. This angle is in the second quadrant.
2. The reference angle for $\theta = \frac{5\pi}{6}$ is $\frac{\pi}{6}$.
3. The sine and cosine of $\frac{\pi}{6}$ are given by $\sin \frac{\pi}{6} = \frac{1}{2}$ and $\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$, respectively.
4. Since $\theta = \frac{5\pi}{6}$ is in the second quadrant, the cosine value will be negative while the sine value remains positive.
Thus, we have:
$\sin \frac{5\pi}{6} = \frac{1}{2}$
$\cos \frac{5\pi}{6} = -\frac{\sqrt{3}}{2}$
Answer 2
Ella Lewis
To determine the sine and cosine of the angle $ heta = frac{5pi}{6}$ using the unit circle:
1. Identify $ heta = frac{5pi}{6}$ on the unit circle, which is in the second quadrant.
2. Find the reference angle, which is $frac{5pi}{6} – pi = frac{-pi}{6}$.
3. For $ heta = frac{-pi}{6}$, we have $sin heta = sin frac{pi}{6} = frac{1}{2}$ and $cos heta = cos frac{pi}{6} = frac{sqrt{3}}{2}$.
4. Adjust the sign according to the quadrant (2nd quadrant):
$sin frac{5pi}{6} = frac{1}{2}$
$cos frac{5pi}{6} = -frac{sqrt{3}}{2}$
Answer 3
Daniel Carter
To compute $sin$ and $cos$ of $ heta = frac{5pi}{6}$ on the unit circle:
Second quadrant: $sin frac{5pi}{6} = frac{1}{2}$ and $cos frac{5pi}{6} = -frac{sqrt{3}}{2}$
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