What is the value of arccos(sin(-(5pi)/6)) ?

The value of arccos(sin(-(5pi)/6)) is (2pi)/3

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arccos(sin(-(5pi)/6))

arccos (sin (- \frac{5 π}{6}))

\frac{2 π}{3}

Solution steps

arccos (sin (- \frac{5 π}{6}))

Use the following property:

sin (- x) = - sin (x)

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

= arccos (- sin (\frac{5 π}{6}))

Rewrite using trig identities:

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

= arccos (- cos (\frac{π}{3}))

Rewrite using trig identities:

cos (\frac{π}{3}) = - cos (\frac{2 π}{3})

= arccos (- (- cos (\frac{2 π}{3})))

Simplify

= arccos (cos (\frac{2 π}{3}))

Use the inverse trig property:

\frac{2 π}{3}

= \frac{2 π}{3}

arcsin (sin (- \frac{3 π}{4}))

30 \cdot cos (4 5^{\circ})

sin (\frac{9}{4} π)

cos (arctan (- \frac{3}{4}))

cos (1 0^{\circ}) cos (2 0^{\circ}) - sin (1 0^{\circ}) sin (2 0^{\circ})

What is the value of arccos(sin(-(5pi)/6)) ?
The value of arccos(sin(-(5pi)/6)) is (2pi)/3