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

The value of arcsin(sin((-pi)/3)) is -pi/3

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arcsin(sin((-pi)/3))

arcsin (sin (\frac{- π}{3}))

- \frac{π}{3}

Decimal Notation

- 60

Solution steps

arcsin (sin (\frac{- π}{3}))

Simplify

= arcsin (sin (- \frac{π}{3}))

Use the following property:

sin (- x) = - sin (x)

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

= arcsin (- sin (\frac{π}{3}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- sin (\frac{π}{3})) = - arcsin (sin (\frac{π}{3}))

= - arcsin (sin (\frac{π}{3}))

Rewrite using trig identities:

arcsin (sin (\frac{π}{3})) = \frac{π}{3}

arcsin (sin (\frac{π}{3}))

For

- \frac{π}{2} \leq x \leq \frac{π}{2}, a rcs in (s in (x)) = x

- \frac{π}{2} \leq \frac{π}{3} \leq \frac{π}{2}

= \frac{π}{3}

= - \frac{π}{3}

cot (- 5)

cot (- 3)

arcsin (\frac{9}{18})

- csc (\frac{π}{3}) cot (\frac{π}{3})

arccos (- \frac{7}{3})

What is the value of arcsin(sin((-pi)/3)) ?
The value of arcsin(sin((-pi)/3)) is -pi/3