Question

compute cot 330

Answer 1

To compute \(\cot(330^\circ)\), we can use the relationship between cotangent and tangent:

\[
\cot(\theta) = \frac{1}{\tan(\theta)}
\]

First, we need to find \(\tan(330^\circ)\).

The angle \(330^\circ\) is in the fourth quadrant, where the tangent function is negative. We can find the reference angle for \(330^\circ\):

\[
360^\circ - 330^\circ = 30^\circ
\]

Now we know that:

\[
\tan(330^\circ) = -\tan(30^\circ)
\]

We know that:

\[
\tan(30^\circ) = \frac{1}{\sqrt{3}}
\]

Thus:

\[
\tan(330^\circ) = -\frac{1}{\sqrt{3}}
\]

Now we can find \(\cot(330^\circ)\):

\[
\cot(330^\circ) = \frac{1}{\tan(330^\circ)} = \frac{1}{-\frac{1}{\sqrt{3}}} = -\sqrt{3}
\]

So, the value of \(\cot(330^\circ)\) is:

\[
\cot(330^\circ) = -\sqrt{3}
\]