Respuesta :
Step-by-step explanation:
We need to find the value of [tex]\tan(\dfrac{5\pi}{6})[/tex]. We can write it as :
[tex]\tan(\dfrac{5\pi}{6})=\tan(\pi -\dfrac{\pi}{6})[/tex]
We know that [tex](\pi -\theta)[/tex] comes in second quadrant. The value of tan is negative. Also, [tex](\pi -\theta)[/tex] do not change. So,
[tex]\tan(\pi -\dfrac{\pi}{6})=\tan(\dfrac{\pi}{6})=\tan30=\dfrac{1}{\sqrt 3}[/tex]
So, the value of [tex]\tan(\dfrac{5\pi}{6})[/tex] is [tex]\dfrac{1}{\sqrt 3}[/tex].
We have find the value of [tex]tan\frac{5\pi }{6}[/tex].
The given function lies in 2nd quadrant.
In the 2nd quadrant value of tanx is negative.
Then ,
[tex]= tan \frac{5\pi }{6} \\\\= tan ( \frac{(6-1)\pi }{6} )\\\\ = tan (\frac{6\pi - \pi }{6} )\\\\= tan (\frac{6\pi }{6} - \frac{\pi }{6} )\\\\= tan ( \pi -\frac{\pi }{6} )[/tex]
We know that , [tex]tan(\pi - \theta )= -tan\theta[/tex]
So,
[tex]= tan ( \pi -\frac{\pi }{6} ) \\\\[/tex]
[tex]= -tan (\frac{\pi }{6} )[/tex]
[tex]tan \frac{5\pi }{6} = - \frac{1}{\sqrt{3} }[/tex]
The value of [tex]tan \frac{5\pi }{6}[/tex] is [tex]\frac{-1}{\sqrt{3} }[/tex] .
For more information about Trigonometry functions click the link given below.
https://brainly.com/question/13944654
