What is the value of tan (pi/6)?

Math Staff asked 9 months ago

Answer:

\[\ tan(\frac{\pi}{6}) = \frac{1}{\sqrt {3}}\]

Explanation:

Using the identity

\[\ tan = \frac{sin}{cos}\]

\[\ sin(\frac{\pi}{6}) = \frac{1}{2}\]

\[\ cos(\frac{\pi}{6}) = \frac{\sqrt {3}}{2}\]

\[\ tan(\frac{\pi}{6}) = \frac{\frac{1}{2}}{\frac{\sqrt {3}}{2}}\]

\[\ tan(\frac{\pi}{6}) = \frac{1}{2} \times \frac{2}{\sqrt {3}}\]

Cancelling the 2‘s and rationalising the denominator

\[\ tan(\frac{\pi}{6}) = \frac{1}{\sqrt {3}}\]

In Decimal

\[\ tan(\frac{\pi}{6}) = 0.577\]