Find the value of $sin( heta)$ for $ heta = frac{7pi}{6}$ using the unit circle.
Answer 1
Joseph Robinson
To find $\sin(\theta)$ for $\theta = \frac{7\pi}{6}$, we need to locate the angle on the unit circle.
First, note that $\frac{7\pi}{6}$ is in the third quadrant where sine is negative.
$\frac{7\pi}{6}$ is $30^\circ$ past $\pi$ (180 degrees).
The reference angle is $30^\circ$ or $\frac{\pi}{6}$.
In the third quadrant, the sine of $\frac{\pi}{6}$ is $-\frac{1}{2}$.
Thus, $\sin(\frac{7\pi}{6}) = -\frac{1}{2}$.
Answer 2
Maria Rodriguez
To determine $sin( heta)$ for $ heta = frac{7pi}{6}$ using the unit circle, follow these steps:
1. Locate the angle $frac{7pi}{6}$ on the unit circle. This angle is in the third quadrant.
2. Since $frac{7pi}{6}$ is $pi + frac{pi}{6}$, we find the reference angle to be $frac{pi}{6}$.
3. In the third quadrant, sine values are negative.
4. The sine of the reference angle $frac{pi}{6}$ is $frac{1}{2}$.
5. Therefore, $sin(frac{7pi}{6}) = -frac{1}{2}$.
Answer 3
Benjamin Clark
To find $sin( heta)$ for $ heta = frac{7pi}{6}$:
1. $ heta = frac{7pi}{6}$ is in the third quadrant.
2. Reference angle: $frac{pi}{6}$.
3. Sine in the third quadrant is negative.
4. Hence, $sin(frac{7pi}{6}) = -frac{1}{2}$.
Start Using PopAi Today