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

The value of sin((pi/2)/3) is 1/2

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sin((pi/2)/3)

sin (\frac{\frac{π}{2}}{3})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (\frac{\frac{π}{2}}{3})

Simplify:

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π}{6}

= sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{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}

4 cos^{2} (\frac{π}{3})

sin^{2} (7.05)

cos (π) 0.534716 ln (0.534716)

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

- 2 sin (π^{1.8}) e^{- 1.8} + 2 π cos (π^{1.8})