What is the value of tan(11/4 pi) ?

The value of tan(11/4 pi) is -1

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tan(11/4 pi)

tan (\frac{11}{4} π)

- 1

Solution steps

tan (\frac{11}{4} π)

Simplify:

\frac{11}{4} π = \frac{11 π}{4}

= tan (\frac{11 π}{4})

tan (\frac{11 π}{4}) = tan (\frac{3 π}{4})

= tan (\frac{3 π}{4})

Rewrite using trig identities:

\frac{sin ( \frac{3 π}{4} )}{cos ( \frac{3 π}{4} )}

= \frac{sin ( \frac{3 π}{4} )}{cos ( \frac{3 π}{4} )}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{\frac{2}{2}}{- \frac{2}{2}}

Simplify

\frac{\frac{2}{2}}{- \frac{2}{2}} : - 1

= - 1

\frac{22}{tan ( 6 0 ^{\circ} )}

arctan (\frac{4.16}{9.8} + 0.4)

arctan (1000000)

tan^{2} (4 5^{\circ} + \frac{25}{2})

\frac{2}{sin ( 1 )}