What is the value of arcsin(sin(13/15 pi)) ?

The value of arcsin(sin(13/15 pi)) is (2pi)/(15)

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arcsin(sin(13/15 pi))

arcsin (sin (\frac{13}{15} π))

\frac{2 π}{15}

Decimal

24

Solution steps

arcsin (sin (\frac{13}{15} π))

Use the inverse trig property:

\frac{2 π}{15}

arcsin (sin (\frac{13}{15} π))

For

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

Rewrite using trig identities:

sin (\frac{13}{15} π) = sin (\frac{2 π}{15})

sin (\frac{13}{15} π)

sin (x) = sin (π - (x))

= sin (π - \frac{13}{15} π)

= sin (\frac{2 π}{15})

= arcsin (sin (\frac{2 π}{15}))

- \frac{π}{2} \leq \frac{2 π}{15} \leq \frac{π}{2}

= \frac{2 π}{15}

= \frac{2 π}{15}

What is the value of arcsin(sin(13/15 pi)) ?
The value of arcsin(sin(13/15 pi)) is (2pi)/(15)