What is the value of arccos(sin(-(4pi)/3)) ?

The value of arccos(sin(-(4pi)/3)) is pi/6

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arccos(sin(-(4pi)/3))

arccos (sin (- \frac{4 π}{3}))

\frac{π}{6}

Solution steps

arccos (sin (- \frac{4 π}{3}))

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{4 π}{3}) = - sin (\frac{4 π}{3})

= arccos (- sin (\frac{4 π}{3}))

Rewrite using trig identities:

sin (\frac{4 π}{3}) = - sin (\frac{2 π}{3})

= arccos (- (- sin (\frac{2 π}{3})))

Simplify

= arccos (sin (\frac{2 π}{3}))

Rewrite using trig identities:

sin (\frac{2 π}{3}) = sin (\frac{π}{3})

= arccos (sin (\frac{π}{3}))

Rewrite using trig identities:

sin (\frac{π}{3}) = cos (\frac{π}{6})

= arccos (cos (\frac{π}{6}))

Use the inverse trig property:

\frac{π}{6}

= \frac{π}{6}

sin (2 arctan (\frac{4}{3}))

sin (21 5^{\circ})

9 sin (\frac{2 π}{3})

6 cos (π)

sin (2 arcsin (\frac{7}{25}))

What is the value of arccos(sin(-(4pi)/3)) ?
The value of arccos(sin(-(4pi)/3)) is pi/6