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

Popular >

tan(-6pi)

tan (- 6 π)

0

Solution steps

tan (- 6 π)

Use the following property:

tan (- x) = - tan (x)

tan (- 6 π) = - tan (6 π)

= - tan (6 π)

tan (6 π) = tan (0)

tan (6 π)

Rewrite

6 π

π \cdot 6 + 0

= tan (π 6 + 0)

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 6 + 0) = tan (0)

= tan (0)

= - tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= - 0

Simplify

= 0

- \frac{π}{2} cos (\frac{π}{2}) + sin (\frac{π}{2})

\frac{2}{π \cdot 0.7} tan (\frac{π \cdot 0.7}{2})

sin (14.4 8^{\circ})

[2 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))]^{3}

637 (cos (3 5^{\circ}))