What is the value of arccos(1/2)+2arcsin(1/2) ?

The value of arccos(1/2)+2arcsin(1/2) is (2pi)/3

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arccos(1/2)+2arcsin(1/2)

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

\frac{2 π}{3}

Decimal Notation

120

Solution steps

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

Use the following trivial identity:

arccos (\frac{1}{2}) = \frac{π}{3}

arccos (\frac{1}{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}{3}

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{6}

arcsin (\frac{1}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{6}

= \frac{π}{3} + 2 \cdot \frac{π}{6}

Simplify

\frac{π}{3} + 2 \cdot \frac{π}{6} : \frac{2 π}{3}

\frac{π}{3} + 2 \cdot \frac{π}{6}

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} + \frac{π}{3}

Apply rule

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

= \frac{π + π}{3}

Add similar elements:

π + π = 2 π

= \frac{2 π}{3}

= \frac{2 π}{3}

\frac{tan ( 30 0 ^{\circ} )}{sin ( 12 0 ^{\circ} )}

cos (\frac{8 π}{7})

15 cos (5 0^{\circ})

arctan (\frac{2}{- 4})

4 + 3 cos (- \frac{π}{3})

What is the value of arccos(1/2)+2arcsin(1/2) ?
The value of arccos(1/2)+2arcsin(1/2) is (2pi)/3