What is the value of csc((25pi)/6) ?

The value of csc((25pi)/6) is 2

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csc((25pi)/6)

csc (\frac{25 π}{6})

2

Solution steps

csc (\frac{25 π}{6})

csc (\frac{25 π}{6}) = csc (\frac{π}{6})

csc (\frac{25 π}{6})

Rewrite

\frac{25 π}{6}

2 π \cdot 2 + \frac{π}{6}

= csc (2 π 2 + \frac{π}{6})

Apply the periodicity of

csc

csc (x + 2 π \cdot k) = csc (x)

csc (2 π \cdot 2 + \frac{π}{6}) = csc (\frac{π}{6})

= csc (\frac{π}{6})

= csc (\frac{π}{6})

Use the following trivial identity:

csc (\frac{π}{6}) = 2

csc (\frac{π}{6})

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= 2

30 cos (5 0^{\circ})

10 cos (36.8 7^{\circ})

- 3 + 4 cos (\frac{π}{2})

cos (\frac{- 3}{2})

sin (0.6435)