Question

4What is tan 11pi/6​

Answer 1

Answer:

$tan(\frac{11\pi}{6}) =-\frac{\sqrt{3} }{3}$

Step-by-step explanation:

Notice that $\frac{11\pi}{6}$ is an angle in the fourth quadrant (where the tangent is negative), and the angle is in fact equivalent to $-\frac{\pi}{6}$. This is one of the special angles for which the sine and cosine functions, as well as the tangent function  have well know values:

Recall that the tangent is defined as

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

and for this angle (  $\frac{11\pi}{6}$ ) the value of the sine and cosine functions are well known:

$sin (\frac{11\pi}{6}) =-\frac{1}{2} \\cos( \frac{11\pi}{6}) =\frac{\sqrt{3} }{2}$

Then, the tangent would be:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\tan(\frac{11\pi}{6}) = \frac{-\frac{1}{2} }{\frac{\sqrt{3} }{2} } \\tan(\frac{11\pi}{6}) =-\frac{1}{\sqrt{3} } \\tan(\frac{11\pi}{6}) =-\frac{\sqrt{3} }{3}$