What is the value of csc((23pi)/4) ?

The value of csc((23pi)/4) is -sqrt(2)

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csc((23pi)/4)

csc (\frac{23 π}{4})

- 2

Solution steps

csc (\frac{23 π}{4})

csc (\frac{23 π}{4}) = csc (\frac{7 π}{4})

= csc (\frac{7 π}{4})

Rewrite using trig identities:

\frac{1}{sin ( \frac{7 π}{4} )}

= \frac{1}{sin ( \frac{7 π}{4} )}

Rewrite using trig identities:

sin (\frac{7 π}{4}) = - \frac{2}{2}

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

Simplify

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

= - 2

2 + 2 sin (\frac{π}{6})

- cot (\frac{π}{4}) + csc (\frac{π}{4})

arcsin (\frac{0}{5})

arcsin (0.385)

16 \cdot cos (4 5^{\circ})