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

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

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arcsin(sin((7pi)/2))

arcsin (sin (\frac{7 π}{2}))

- \frac{π}{2}

Decimal

- 90

Solution steps

arcsin (sin (\frac{7 π}{2}))

Use the inverse trig property:

- \frac{π}{2}

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

sin (\frac{7 π}{2})

sin (x + 2 π \cdot k) = sin (x)

= sin (\frac{7 π}{2} - 2 \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}

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