What is the value of csc(2((3pi)/8)) ?

The value of csc(2((3pi)/8)) is square root of 2

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csc(2((3pi)/8))

csc (2 (\frac{3 π}{8}))

2

Solution steps

csc (2 (\frac{3 π}{8}))

= csc (2 \cdot \frac{3 π}{8})

Simplify:

2 \cdot \frac{3 π}{8} = \frac{3 π}{4}

= csc (\frac{3 π}{4})

Rewrite using trig identities:

\frac{1}{sin ( \frac{3 π}{4} )}

= \frac{1}{sin ( \frac{3 π}{4} )}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

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

= 2

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

2 - cos (\frac{π}{2})

sec (- \frac{13 π}{4})

arccos (\frac{4}{4 2})

- 2 sec (9 0^{\circ})

What is the value of csc(2((3pi)/8)) ?
The value of csc(2((3pi)/8)) is square root of 2