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

The value of csc(-pi/3) is -(2sqrt(3))/3

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csc(-pi/3)

csc (- \frac{π}{3})

- \frac{2 3}{3}

Decimal Notation

- 1.15470 \dots

Solution steps

csc (- \frac{π}{3})

Use the following property:

csc (- x) = - csc (x)

csc (- \frac{π}{3}) = - csc (\frac{π}{3})

= - csc (\frac{π}{3})

Use the following trivial identity:

csc (\frac{π}{3}) = \frac{2 3}{3}

csc (\frac{π}{3})

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

= \frac{2 3}{3}

= - \frac{2 3}{3}

3 sin (π)

arccos (- \frac{3}{5})

10 cos (6 0^{\circ})

tan (- \frac{7 π}{4})

tan (4 4^{\circ})