What is the value of arcsin(sin((7pi)/9)) ?

The value of arcsin(sin((7pi)/9)) is (2pi)/9

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arcsin(sin((7pi)/9))

arcsin (sin (\frac{7 π}{9}))

\frac{2 π}{9}

Decimal

40

Solution steps

arcsin (sin (\frac{7 π}{9}))

Use the inverse trig property:

\frac{2 π}{9}

arcsin (sin (\frac{7 π}{9}))

For

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

Rewrite using trig identities:

sin (\frac{7 π}{9}) = sin (\frac{2 π}{9})

sin (\frac{7 π}{9})

sin (x) = sin (π - (x))

= sin (π - \frac{7 π}{9})

= sin (\frac{2 π}{9})

= arcsin (sin (\frac{2 π}{9}))

- \frac{π}{2} \leq \frac{2 π}{9} \leq \frac{π}{2}

= \frac{2 π}{9}

= \frac{2 π}{9}

What is the value of arcsin(sin((7pi)/9)) ?
The value of arcsin(sin((7pi)/9)) is (2pi)/9