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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc((-pi)/3)

csc (\frac{- π}{3})

- \frac{2 3}{3}

Decimal Notation

- 1.15470 \dots

Solution steps

csc (\frac{- π}{3})

Simplify

= 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}

120 sin (3 0^{\circ})

csc (\frac{- π}{2})

sin (arcsin (\frac{8}{17}) + arccos (- \frac{3}{5}))

8 \cdot cos (4 0^{\circ})

1 - cos (\frac{π}{6})