What is the value of tan(-5pi) ?

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tan(-5pi)

tan (- 5 π)

0

Solution steps

tan (- 5 π)

Use the following property:

tan (- x) = - tan (x)

tan (- 5 π) = - tan (5 π)

= - tan (5 π)

tan (5 π) = tan (0)

tan (5 π)

Rewrite

5 π

π \cdot 5 + 0

= tan (π 5 + 0)

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 5 + 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

- csc^{2} (\frac{π}{3})

cos (\frac{- 11 π}{6})

4 cos (1)

4 cos (4)

cos (12 0^{\circ}) cos (3 0^{\circ}) + sin (12 0^{\circ}) sin (3 0^{\circ})