What is the value of arcsin(sin((3pi)/5)) ?

The value of arcsin(sin((3pi)/5)) is (2pi)/5

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arcsin(sin((3pi)/5))

arcsin (sin (\frac{3 π}{5}))

\frac{2 π}{5}

Decimal Notation

72

Solution steps

arcsin (sin (\frac{3 π}{5}))

Use the inverse trig property:

\frac{2 π}{5}

arcsin (sin (\frac{3 π}{5}))

For

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

Rewrite using trig identities:

sin (\frac{3 π}{5}) = sin (\frac{2 π}{5})

sin (\frac{3 π}{5})

sin (x) = sin (π - (x))

= sin (π - \frac{3 π}{5})

= sin (\frac{2 π}{5})

= arcsin (sin (\frac{2 π}{5}))

- \frac{π}{2} \leq \frac{2 π}{5} \leq \frac{π}{2}

= \frac{2 π}{5}

= \frac{2 π}{5}

cos (20 0^{\circ})

2 cos (\frac{11 π}{6})

sin (12 5^{\circ})

- arctan (1)

sin (6 7^{\circ})

What is the value of arcsin(sin((3pi)/5)) ?
The value of arcsin(sin((3pi)/5)) is (2pi)/5