What is the value of tan(5*(9pi)/5) ?

The value of tan(5*(9pi)/5) is 0

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tan(5*(9pi)/5)

tan (5 \cdot \frac{9 π}{5})

0

Solution steps

tan (5 \cdot \frac{9 π}{5})

Simplify:

5 \cdot \frac{9 π}{5} = 9 π

5 \cdot \frac{9 π}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{9 π 5}{5}

Cancel the common factor:

5

= 9 π

= tan (9 π)

tan (9 π) = tan (0)

tan (9 π)

Rewrite

9 π

π \cdot 9 + 0

= tan (π 9 + 0)

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 9 + 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

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