What is the value of tan((11pi)/(16)) ?

The value of tan((11pi)/(16)) is -sqrt(4\sqrt{2-\sqrt{2)}-2sqrt(2)sqrt(2-\sqrt{2)}+7-4sqrt(2)}

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tan((11pi)/(16))

tan (\frac{11 π}{16})

- 4 2 - 2 - 22 2 - 2 + 7 - 42

Solution steps

tan (\frac{11 π}{16})

Rewrite using trig identities:

- \frac{1 - cos ( \frac{11 π}{8} )}{1 + cos ( \frac{11 π}{8} )}

= - \frac{1 - cos ( \frac{11 π}{8} )}{1 + cos ( \frac{11 π}{8} )}

Rewrite using trig identities:

cos (\frac{11 π}{8}) = - \frac{2 - 2}{2}

= - \frac{1 - ( - \frac{2 - 2}{2} )}{1 - \frac{2 - 2}{2}}

Simplify

- \frac{1 - ( - \frac{2 - 2}{2} )}{1 - \frac{2 - 2}{2}} : - 4 2 - 2 - 22 2 - 2 + 7 - 42

= - 4 2 - 2 - 22 2 - 2 + 7 - 42

tan (141 0^{\circ})

e^{1} - 2 cos (1)

cos^{2} (\frac{9 π}{8}) - cos (2 \cdot \frac{9 π}{8})

sin (- 132 0^{\circ})

3 cos (4)

What is the value of tan((11pi)/(16)) ?
The value of tan((11pi)/(16)) is -sqrt(4\sqrt{2-\sqrt{2)}-2sqrt(2)sqrt(2-\sqrt{2)}+7-4sqrt(2)}