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

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

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arccos(sin(-(2pi)/3))

arccos (sin (- \frac{2 π}{3}))

\frac{5 π}{6}

Solution steps

arccos (sin (- \frac{2 π}{3}))

Use the following property:

sin (- x) = - sin (x)

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

= 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}) = - sin (\frac{5 π}{3})

= arccos (- (- sin (\frac{5 π}{3})))

Simplify

= arccos (sin (\frac{5 π}{3}))

Rewrite using trig identities:

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

= arccos (cos (- \frac{7 π}{6}))

Use the inverse trig property:

\frac{5 π}{6}

= \frac{5 π}{6}

20 cos (\frac{2 π}{3})

\frac{250}{sin ( 4 5 ^{\circ} )}

arctan (\frac{11.2}{18.3})

arctan (\frac{- 1.34}{0.84})

\frac{7}{tan ( 5 0 ^{\circ} )}

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