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

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

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arcsin(sin(-(5pi)/2))

arcsin (sin (- \frac{5 π}{2}))

- \frac{π}{2}

Decimal Notation

- 90

Solution steps

arcsin (sin (- \frac{5 π}{2}))

Use the inverse trig property:

- \frac{π}{2}

arcsin (sin (- \frac{5 π}{2}))

For

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

Rewrite using trig identities:

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

sin (- \frac{5 π}{2})

sin (x + 2 π \cdot k) = sin (x)

= sin (- \frac{5 π}{2} + 1 \cdot 2 π)

= sin (- \frac{π}{2})

= arcsin (sin (- \frac{π}{2}))

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

= - \frac{π}{2}

= - \frac{π}{2}

arctan (\frac{15}{12})

\frac{arctan ^{2} ( 1 )}{2}

sin (\frac{7}{12 π}) - cos (\frac{π}{12})

arcsec (1.2)

4 + 3 cos (\frac{π}{6})

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