What is the value of arcsin(sin(-3.5)) ?

The value of arcsin(sin(-3.5)) is (7-2pi)/2

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arcsin(sin(-3.5))

arcsin (sin (- 3.5))

\frac{7 - 2 π}{2}

Decimal Notation

20.54

Solution steps

arcsin (sin (- 3.5))

= arcsin (sin (- \frac{7}{2}))

Use the inverse trig property:

\frac{7 - 2 π}{2}

arcsin (sin (- \frac{7}{2}))

For

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

Rewrite using trig identities:

sin (- \frac{7}{2}) = sin (\frac{7 - 2 π}{2})

sin (- \frac{7}{2})

sin (x) = sin (π - (x))

= sin (\frac{7}{2} - π)

= sin (\frac{7 - 2 π}{2})

= arcsin (sin (\frac{7 - 2 π}{2}))

- \frac{π}{2} \leq \frac{7 - 2 π}{2} \leq \frac{π}{2}

= \frac{7 - 2 π}{2}

= \frac{7 - 2 π}{2}

8 cos (29 0^{\circ}) + 6 cos (6 0^{\circ})

sin (\frac{11}{12})

0 - arctan (0)

arcsin (\frac{3}{11})

sin (arcsin (6))

What is the value of arcsin(sin(-3.5)) ?
The value of arcsin(sin(-3.5)) is (7-2pi)/2