What is the value of $sin(frac{pi}{6})$ and $cos(frac{pi}{6})$ on the unit circle?
Answer 1
Lily Perez
To find the values of $\sin(\frac{\pi}{6})$ and $\cos(\frac{\pi}{6})$ on the unit circle, we need to understand the coordinates of the point on the unit circle corresponding to the angle $\frac{\pi}{6}$. The unit circle has a radius of 1, and the coordinates at an angle $\theta$ are $(\cos(\theta), \sin(\theta))$.
For $\theta = \frac{\pi}{6}$:
The coordinates on the unit circle are $\left(\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6})\right)$.
From the unit circle chart:
$\cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$
$\sin(\frac{\pi}{6}) = \frac{1}{2}$
Therefore, $\sin(\frac{\pi}{6}) = \frac{1}{2}$ and $\cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$.
Answer 2
Amelia Mitchell
We can determine the values of $sin(frac{pi}{6})$ and $cos(frac{pi}{6})$ by looking at the coordinates of the corresponding point on the unit circle. The formula for finding these values on the unit circle is to use the coordinates $(cos( heta), sin( heta))$ where $ heta$ is the angle.
When $ heta = frac{pi}{6}$, we know from the unit circle:
$cos(frac{pi}{6}) = frac{sqrt{3}}{2}$
$sin(frac{pi}{6}) = frac{1}{2}$
So, $sin(frac{pi}{6}) = frac{1}{2}$ and $cos(frac{pi}{6}) = frac{sqrt{3}}{2}$.
Answer 3
Emily Hall
The values of $sin(frac{pi}{6})$ and $cos(frac{pi}{6})$ can be directly read from the unit circle:
$sin(frac{pi}{6}) = frac{1}{2}$
$cos(frac{pi}{6}) = frac{sqrt{3}}{2}$
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