If $\theta=\frac{\pi}{6}$, find the following. Give exact answers.
\[
\sin (\theta)=
\]
\[
\cos (\theta)=
\]

Answer

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Final Answer: $\cos (\theta)=\boxed{\frac{\sqrt{3}}{2}}$

Steps

Step 1 ：The question is asking for the sine and cosine of the angle $\theta=\frac{\pi}{6}$. These are standard angles in trigonometry and their sine and cosine values are well known.

Step 2 ：The exact values for $\sin(\frac{\pi}{6})$ and $\cos(\frac{\pi}{6})$ are $\frac{1}{2}$ and $\frac{\sqrt{3}}{2}$ respectively.

Step 3 ：Final Answer: $\sin (\theta)=\boxed{\frac{1}{2}}$

Step 4 ：Final Answer: $\cos (\theta)=\boxed{\frac{\sqrt{3}}{2}}$

If $\theta=\frac{\pi}{6}$, find the following. Give exact answers.\[\sin (\theta)=\]\[\cos (\theta)=\]

Answer

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If $\theta=\frac{\pi}{6}$, find the following. Give exact answers.
\[
\sin (\theta)=
\]
\[
\cos (\theta)=
\]