What is the value of csc(-(7pi)/3) ?

The value of csc(-(7pi)/3) is -(2sqrt(3))/3

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csc(-(7pi)/3)

csc (- \frac{7 π}{3})

- \frac{2 3}{3}

Decimal Notation

- 1.15470 \dots

Solution steps

csc (- \frac{7 π}{3})

Use the following property:

csc (- x) = - csc (x)

csc (- \frac{7 π}{3}) = - csc (\frac{7 π}{3})

= - csc (\frac{7 π}{3})

csc (\frac{7 π}{3}) = csc (\frac{π}{3})

csc (\frac{7 π}{3})

Rewrite

\frac{7 π}{3}

2 π + \frac{π}{3}

= csc (2 π + \frac{π}{3})

Apply the periodicity of

csc

csc (x + 2 π) = csc (x)

csc (2 π + \frac{π}{3}) = 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}

csc (6 π)

tan (\frac{25 π}{4})

e^{- 1} sin (1)

cos^{2} (4 5^{\circ}) + sin^{2} (4 5^{\circ})

\frac{2 tan ( 4 2 ^{\circ} )}{1 - tan ( 4 2 ^{\circ} )}

What is the value of csc(-(7pi)/3) ?
The value of csc(-(7pi)/3) is -(2sqrt(3))/3