What is the value of arcsin(sin((3pi)/4)) ?

The value of arcsin(sin((3pi)/4)) is pi/4

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arcsin(sin((3pi)/4))

arcsin (sin (\frac{3 π}{4}))

\frac{π}{4}

Decimal Notation

45

Solution steps

arcsin (sin (\frac{3 π}{4}))

Use the inverse trig property:

\frac{π}{4}

arcsin (sin (\frac{3 π}{4}))

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}{4}) = sin (\frac{π}{4})

sin (\frac{3 π}{4})

sin (x) = sin (π - (x))

= sin (π - \frac{3 π}{4})

= sin (\frac{π}{4})

= arcsin (sin (\frac{π}{4}))

- \frac{π}{2} \leq \frac{π}{4} \leq \frac{π}{2}

= \frac{π}{4}

= \frac{π}{4}

sin (2 θ) = 2 sin (θ) cos (θ)

sin (2 x) + sin (x) = 0

sec^{2} (x) - tan^{2} (x) = 1

arcsin (sin (\frac{5 π}{4}))

sin^{2} (π)

What is the value of arcsin(sin((3pi)/4)) ?
The value of arcsin(sin((3pi)/4)) is pi/4