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

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

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arcsin(cos((5pi)/6))

arcsin (cos (\frac{5 π}{6}))

- \frac{π}{3}

Decimal Notation

- 60

Solution steps

arcsin (cos (\frac{5 π}{6}))

Rewrite using trig identities:

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

cos (\frac{5 π}{6})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{5 π}{6})

= sin (- \frac{π}{3})

= arcsin (sin (- \frac{π}{3}))

Use the inverse trig property:

- \frac{π}{3}

arcsin (sin (- \frac{π}{3}))

For

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

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

= - \frac{π}{3}

= - \frac{π}{3}

cos (5 6^{\circ})

arccos (0.95)

arcsin (\frac{3}{2})

2 cos (2)

arctan (45)

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