What is the value of tan((21pi)/4) ?

The value of tan((21pi)/4) is 1

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tan((21pi)/4)

tan (\frac{21 π}{4})

1

Solution steps

tan (\frac{21 π}{4})

tan (\frac{21 π}{4}) = tan (\frac{π}{4})

tan (\frac{21 π}{4})

Rewrite

\frac{21 π}{4}

π \cdot 5 + \frac{π}{4}

= tan (π 5 + \frac{π}{4})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 5 + \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

sec (- 30 0^{\circ})

sin (arccos (- 1))

csc (arctan (- 1))

arcsin (\frac{14}{16})

(tan (40 5^{\circ}) + cos (56 0^{\circ})) (sin (81 0^{\circ}) + cos (106 0^{\circ}))