What is the value of csc(-(9pi)/2) ?

The value of csc(-(9pi)/2) is -1

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csc(-(9pi)/2)

csc (- \frac{9 π}{2})

- 1

Solution steps

csc (- \frac{9 π}{2})

Use the following property:

csc (- x) = - csc (x)

csc (- \frac{9 π}{2}) = - csc (\frac{9 π}{2})

= - csc (\frac{9 π}{2})

csc (\frac{9 π}{2}) = csc (\frac{π}{2})

csc (\frac{9 π}{2})

Rewrite

\frac{9 π}{2}

2 π \cdot 2 + \frac{π}{2}

= csc (2 π 2 + \frac{π}{2})

Apply the periodicity of

csc

csc (x + 2 π \cdot k) = csc (x)

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

= csc (\frac{π}{2})

= - csc (\frac{π}{2})

Use the following trivial identity:

csc (\frac{π}{2}) = 1

csc (\frac{π}{2})

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

= 1

= - 1

- sin (π) + cos (π)

arctan (\frac{324}{54})

sin (- \frac{π}{12}) csc (\frac{25 π}{12})

80 \cdot cos (6 0^{\circ})

arcsin (\frac{16}{34})