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quester [9]
3 years ago
14

4What is tan 11pi/6​

Mathematics
1 answer:
Vikentia [17]3 years ago
8 0

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}

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