What is the value of csc((13pi)/8) ?

The value of csc((13pi)/8) is -2sqrt(2+\sqrt{2)}+sqrt(2)sqrt(2+\sqrt{2)}

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csc((13pi)/8)

csc (\frac{13 π}{8})

- 2 2 + 2 + 2 2 + 2

Solution steps

csc (\frac{13 π}{8})

Rewrite using trig identities:

\frac{1}{sin ( \frac{13 π}{8} )}

= \frac{1}{sin ( \frac{13 π}{8} )}

Rewrite using trig identities:

sin (\frac{13 π}{8}) = - \frac{2 + 2}{2}

= \frac{1}{- \frac{2 + 2}{2}}

Simplify

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

= - 2 2 + 2 + 2 2 + 2

cos (- 7 0^{\circ})

\frac{5 sin ( 3 6 ^{\circ} )}{8}

\frac{13}{tan ( 2 7 ^{\circ} )}

cot (- \frac{7 π}{3})

\frac{6.3}{cos ( 2 7 ^{\circ} )}

What is the value of csc((13pi)/8) ?
The value of csc((13pi)/8) is -2sqrt(2+\sqrt{2)}+sqrt(2)sqrt(2+\sqrt{2)}