What is the value of csc((-9pi)/4) ?

The value of csc((-9pi)/4) is -sqrt(2)

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csc((-9pi)/4)

csc (\frac{- 9 π}{4})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

csc (\frac{- 9 π}{4})

Simplify

= csc (- \frac{9 π}{4})

Use the following property:

csc (- x) = - csc (x)

csc (- \frac{9 π}{4}) = - csc (\frac{9 π}{4})

= - csc (\frac{9 π}{4})

csc (\frac{9 π}{4}) = csc (\frac{π}{4})

csc (\frac{9 π}{4})

Rewrite

\frac{9 π}{4}

2 π + \frac{π}{4}

= csc (2 π + \frac{π}{4})

Apply the periodicity of

csc

csc (x + 2 π) = csc (x)

csc (2 π + \frac{π}{4}) = csc (\frac{π}{4})

= csc (\frac{π}{4})

= - csc (\frac{π}{4})

Use the following trivial identity:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

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

5 cot (3 0^{\circ})

arctan (\frac{88.49}{201})

2 \cdot (- 2.021) - 10 \cdot sin (- 2.021)

cos (- \frac{π}{7})

tan^{2} (4 5^{\circ} + \frac{31}{2})