What is the value of arccsc((-2)/(sqrt(3))) ?

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

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arccsc((-2)/(sqrt(3)))

arccsc (\frac{- 2}{3})

- \frac{π}{3}

Decimal Notation

- 60

Solution steps

arccsc (\frac{- 2}{3})

Simplify:

\frac{- 2}{3} = - \frac{2 3}{3}

\frac{- 2}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{3}

Rationalize

- \frac{2}{3} : - \frac{2 3}{3}

- \frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

= arccsc (- \frac{2 3}{3})

Use the following property:

arccsc (- x) = - arccsc (x)

arccsc (- \frac{2 3}{3}) = - arccsc (\frac{2 3}{3})

= - arccsc (\frac{2 3}{3})

Use the following trivial identity:

arccsc (\frac{2 3}{3}) = \frac{π}{3}

arccsc (\frac{2 3}{3})

x 22 \frac{2 3}{3} 1 arccsc (x) \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arccsc (x) 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{3}

= - \frac{π}{3}

- \frac{1}{sin ^{2} ( 6 0 ^{\circ} )}

- 2 sin (2 (\frac{π}{4}))

sin (arctan (\frac{3}{2}))

2 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))

tan (33.6 9^{\circ})

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