What is the value of arcsin(sin((11pi)/8)) ?

The value of arcsin(sin((11pi)/8)) is -(3pi)/8

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arcsin(sin((11pi)/8))

arcsin (sin (\frac{11 π}{8}))

- \frac{3 π}{8}

Decimal Notation

- 67.5

Solution steps

arcsin (sin (\frac{11 π}{8}))

Use the inverse trig property:

- \frac{3 π}{8}

arcsin (sin (\frac{11 π}{8}))

For

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

Rewrite using trig identities:

sin (\frac{11 π}{8}) = sin (- \frac{3 π}{8})

sin (\frac{11 π}{8})

sin (x) = sin (π - (x))

= sin (π - \frac{11 π}{8})

= sin (- \frac{3 π}{8})

= arcsin (sin (- \frac{3 π}{8}))

- \frac{π}{2} \leq - \frac{3 π}{8} \leq \frac{π}{2}

= - \frac{3 π}{8}

= - \frac{3 π}{8}

sin (17 0^{\circ})

arcsin (\frac{3}{4})

cot (0) \cdot sin (0)

2 cos^{2} (\frac{5 π}{8}) - 1

2 sin (4)

What is the value of arcsin(sin((11pi)/8)) ?
The value of arcsin(sin((11pi)/8)) is -(3pi)/8