What is the value of sin((10pi)/(12)) ?

The value of sin((10pi)/(12)) is 1/2

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sin((10pi)/(12))

sin (\frac{10 π}{12})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (\frac{10 π}{12})

Simplify:

\frac{10 π}{12} = \frac{5 π}{6}

\frac{10 π}{12}

Cancel the common factor:

2

= \frac{5 π}{6}

= sin (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (\frac{5 π}{6})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

arctan (\frac{- 12}{9})

sin (5 0^{\circ}) \cdot 2

arctan (\frac{1}{25})

4.7 \cdot cos^{2} (11 0^{\circ})

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