Question

Which of the following is equivalent to tan(5pi/6)

Answer 1

Step-by-step explanation:

We need to find the value of $\tan(\dfrac{5\pi}{6})$. We can write it as :

$\tan(\dfrac{5\pi}{6})=\tan(\pi -\dfrac{\pi}{6})$

We know that $(\pi -\theta)$ comes in second quadrant. The value of tan is negative. Also, $(\pi -\theta)$ do not change. So,

$\tan(\pi -\dfrac{\pi}{6})=\tan(\dfrac{\pi}{6})=\tan30=\dfrac{1}{\sqrt 3}$

So, the value of $\tan(\dfrac{5\pi}{6})$ is $\dfrac{1}{\sqrt 3}$.