What is the value of arccos(cos((7pi)/6)) ?

The value of arccos(cos((7pi)/6)) is (5pi)/6

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arccos(cos((7pi)/6))

arccos (cos (\frac{7 π}{6}))

\frac{5 π}{6}

Decimal Notation

150

Solution steps

arccos (cos (\frac{7 π}{6}))

Use the inverse trig property:

\frac{5 π}{6}

arccos (cos (\frac{7 π}{6}))

For

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

Rewrite using trig identities:

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

cos (\frac{7 π}{6})

cos (x) = cos (2 π - (x))

= cos (2 π - \frac{7 π}{6})

= cos (\frac{5 π}{6})

= arccos (cos (\frac{5 π}{6}))

0 \leq \frac{5 π}{6} \leq π

= \frac{5 π}{6}

= \frac{5 π}{6}

cos (6 0^{\circ})

sin^{2} (2 x) = 1

arctan (- \frac{240}{180})

sin (\frac{7 π}{12})

arccos (\frac{8}{20})

What is the value of arccos(cos((7pi)/6)) ?
The value of arccos(cos((7pi)/6)) is (5pi)/6