What is the value of arccos(sin((5pi)/3)) ?

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

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arccos(sin((5pi)/3))

arccos (sin (\frac{5 π}{3}))

\frac{5 π}{6}

Decimal Notation

150

Solution steps

arccos (sin (\frac{5 π}{3}))

Rewrite using trig identities:

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

sin (\frac{5 π}{3})

cos (\frac{π}{2} - x) = sin (x)

= cos (\frac{π}{2} - \frac{5 π}{3})

= cos (- \frac{7 π}{6})

= 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 + 2 π \cdot k) = cos (x)

= cos (- \frac{7 π}{6} + 1 \cdot 2 π)

= 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}

\frac{tan ( 2 0 ^{\circ} ) + tan ( 1 0 ^{\circ} )}{1 - tan ( 2 0 ^{\circ} ) tan ( 1 0 ^{\circ} )}

cos (2 \cdot 0)

tan (2 8^{\circ})

cos (π^{2})

arctan (tan (\frac{5 π}{4}))

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