What is the value of arcsin(cos((5pi)/3)) ?

The value of arcsin(cos((5pi)/3)) is pi/6

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arcsin(cos((5pi)/3))

arcsin (cos (\frac{5 π}{3}))

\frac{π}{6}

Decimal Notation

30

Solution steps

arcsin (cos (\frac{5 π}{3}))

Rewrite using trig identities:

cos (\frac{5 π}{3}) = sin (- \frac{7 π}{6})

cos (\frac{5 π}{3})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{5 π}{3})

= sin (- \frac{7 π}{6})

= arcsin (sin (- \frac{7 π}{6}))

Use the inverse trig property:

\frac{π}{6}

arcsin (sin (- \frac{7 π}{6}))

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}{6}) = sin (\frac{π}{6})

sin (- \frac{7 π}{6})

sin (x) = sin (π - (x))

= sin (\frac{7 π}{6} - π)

= sin (\frac{π}{6})

= arcsin (sin (\frac{π}{6}))

- \frac{π}{2} \leq \frac{π}{6} \leq \frac{π}{2}

= \frac{π}{6}

= \frac{π}{6}

sec (\frac{9 π}{2})

arcsin (- 2)

sin (\frac{π}{2}) cos (\frac{π}{6}) - cos (\frac{π}{2}) sin (\frac{π}{6})

sin (10 4^{\circ})

sin (1.57)

What is the value of arcsin(cos((5pi)/3)) ?
The value of arcsin(cos((5pi)/3)) is pi/6