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

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

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arccos(sin((5pi)/6))

arccos (sin (\frac{5 π}{6}))

\frac{π}{3}

Decimal Notation

60

Solution steps

arccos (sin (\frac{5 π}{6}))

Rewrite using trig identities:

sin (\frac{5 π}{6}) = sin (\frac{π}{6})

sin (\frac{5 π}{6})

Use the basic trigonometric identity:

sin (x) = sin (π - x)

= sin (π - \frac{5 π}{6})

Simplify:

π - \frac{5 π}{6} = \frac{π}{6}

π - \frac{5 π}{6}

Convert element to fraction:

π = \frac{π 6}{6}

= \frac{π 6}{6} - \frac{5 π}{6}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π 6 - 5 π}{6}

Add similar elements:

6 π - 5 π = π

= \frac{π}{6}

= sin (\frac{π}{6})

= arccos (sin (\frac{π}{6}))

Rewrite using trig identities:

sin (\frac{π}{6}) = cos (\frac{π}{3})

sin (\frac{π}{6})

cos (\frac{π}{2} - x) = sin (x)

= cos (\frac{π}{2} - \frac{π}{6})

= cos (\frac{π}{3})

= arccos (cos (\frac{π}{3}))

Use the inverse trig property:

\frac{π}{3}

arccos (cos (\frac{π}{3}))

For

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

0 \leq \frac{π}{3} \leq π

= \frac{π}{3}

= \frac{π}{3}

tan (5 7^{\circ})

sin (6 8^{\circ})

cos (0 π)

30 sin (3 0^{\circ})

cos (\frac{4}{3} π)

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