What is the value of tan(-(9pi)/4) ?

The value of tan(-(9pi)/4) is -1

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tan(-(9pi)/4)

tan (- \frac{9 π}{4})

- 1

Solution steps

tan (- \frac{9 π}{4})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{9 π}{4}) = - tan (\frac{9 π}{4})

= - tan (\frac{9 π}{4})

tan (\frac{9 π}{4}) = tan (\frac{π}{4})

tan (\frac{9 π}{4})

Rewrite

\frac{9 π}{4}

π \cdot 2 + \frac{π}{4}

= tan (π 2 + \frac{π}{4})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 2 + \frac{π}{4}) = tan (\frac{π}{4})

= tan (\frac{π}{4})

= - tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

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}

= 1

= - 1

tan (6 9^{\circ})

tan (\frac{31 π}{6})

40 \cdot sin (6 0^{\circ})

15 cos (4 5^{\circ})

10 \cdot sin (6 0^{\circ})