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

The value of arccos(cos((4pi)/3)) is (2pi)/3

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arccos(cos((4pi)/3))

arccos (cos (\frac{4 π}{3}))

\frac{2 π}{3}

Decimal Notation

120

Solution steps

arccos (cos (\frac{4 π}{3}))

Use the inverse trig property:

\frac{2 π}{3}

arccos (cos (\frac{4 π}{3}))

For

0 \leq x \leq π, a rccos (cos (x)) = x

Rewrite using trig identities:

cos (\frac{4 π}{3}) = cos (\frac{2 π}{3})

cos (\frac{4 π}{3})

cos (x) = cos (2 π - (x))

= cos (2 π - \frac{4 π}{3})

= cos (\frac{2 π}{3})

= arccos (cos (\frac{2 π}{3}))

0 \leq \frac{2 π}{3} \leq π

= \frac{2 π}{3}

= \frac{2 π}{3}

2 cos^{2} (x) - cos (x) - 1 = 0

arcsin (- \frac{1}{2})

csc (- \frac{5 π}{6})

tan (\frac{5 π}{6})

3 cot^{2} (x) - 1 = 0

What is the value of arccos(cos((4pi)/3)) ?
The value of arccos(cos((4pi)/3)) is (2pi)/3