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

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

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arcsin((sqrt(3))/2)+arccos(1/2)

arcsin (\frac{3}{2}) + arccos (\frac{1}{2})

\frac{2 π}{3}

Decimal Notation

120

Solution steps

arcsin (\frac{3}{2}) + arccos (\frac{1}{2})

Use the following trivial identity:

arcsin (\frac{3}{2}) = \frac{π}{3}

arcsin (\frac{3}{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}{3}

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}

= \frac{π}{3} + \frac{π}{3}

Simplify

\frac{π}{3} + \frac{π}{3} : \frac{2 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}

sec (arctan (\frac{6}{7}))

- cos (4 π)

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

4 sec^{2} (0)

csc (\frac{- 5 π}{6})

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