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 Notation

- 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 (\frac{7 π}{9} - π)

= 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}

16 cos (0)

cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4})

cos (1) + i sin (1)

3 cos (13 5^{\circ})

1 - 2 sin^{2} (\frac{π}{7})

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