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

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

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

arccos (sin (\frac{2 π}{3}))

\frac{π}{6}

Decimal Notation

30

Solution steps

arccos (sin (\frac{2 π}{3}))

Rewrite using trig identities:

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

sin (\frac{2 π}{3})

Use the basic trigonometric identity:

sin (x) = sin (π - x)

= sin (π - \frac{2 π}{3})

Simplify:

π - \frac{2 π}{3} = \frac{π}{3}

π - \frac{2 π}{3}

Convert element to fraction:

π = \frac{π 3}{3}

= \frac{π 3}{3} - \frac{2 π}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{π 3 - 2 π}{3}

Add similar elements:

3 π - 2 π = π

= \frac{π}{3}

= sin (\frac{π}{3})

= arccos (sin (\frac{π}{3}))

Rewrite using trig identities:

sin (\frac{π}{3}) = cos (\frac{π}{6})

sin (\frac{π}{3})

cos (\frac{π}{2} - x) = sin (x)

= cos (\frac{π}{2} - \frac{π}{3})

= cos (\frac{π}{6})

= arccos (cos (\frac{π}{6}))

Use the inverse trig property:

\frac{π}{6}

arccos (cos (\frac{π}{6}))

For

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

0 \leq \frac{π}{6} \leq π

= \frac{π}{6}

= \frac{π}{6}

sin^{2} (0.5)

arctan (\frac{2 π}{3})

arcsin (\frac{5}{3})

tan (\frac{14 π}{3})

4 sin (4)

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