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

The value of 2arccos((sqrt(3))/2) is pi/3

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2arccos((sqrt(3))/2)

2 arccos (\frac{3}{2})

\frac{π}{3}

Decimal Notation

60

Solution steps

2 arccos (\frac{3}{2})

Use the following trivial identity:

arccos (\frac{3}{2}) = \frac{π}{6}

arccos (\frac{3}{2})

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{6}

= 2 \cdot \frac{π}{6}

Simplify

2 \cdot \frac{π}{6} : \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

= \frac{π}{3}

sin (\frac{1}{( \frac{2}{3 π} )})

cos (arctan (- \frac{20}{21}))

cos (16. 2^{\circ})

sin (\frac{π}{8}) cos (\frac{π}{8})

cos (3 (\frac{π}{6}))

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