What is the value of csc(255) ?

The value of csc(255) is sqrt(2)-sqrt(6)

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csc(255)

csc (25 5^{\circ})

2 - 6

Solution steps

csc (25 5^{\circ})

Rewrite using trig identities:

\frac{1}{sin ( 25 5 ^{\circ} )}

= \frac{1}{sin ( 25 5 ^{\circ} )}

Rewrite using trig identities:

sin (25 5^{\circ}) = \frac{- 2 - 6}{4}

= \frac{1}{\frac{- 2 - 6}{4}}

Simplify

\frac{1}{\frac{- 2 - 6}{4}} : 2 - 6

= 2 - 6

\frac{1}{tan ( 2 0 ^{\circ} )}

arctan (\frac{6.88}{9.8} + 0.1)

arctan (\frac{- 8}{5})

2 sin (33 0^{\circ})

\frac{2 \cdot 1.5 \cdot 9.78}{sin ^{2} ( 1 0 ^{\circ} )}