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

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

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(sin(pi/3))/(pi/3)

\frac{sin ( \frac{π}{3} )}{\frac{π}{3}}

\frac{3 3}{2 π}

Decimal Notation

0.82699 \dots

Solution steps

\frac{sin ( \frac{π}{3} )}{\frac{π}{3}}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

= \frac{\frac{3}{2}}{\frac{π}{3}}

Simplify

\frac{\frac{3}{2}}{\frac{π}{3}} : \frac{3 3}{2 π}

\frac{\frac{3}{2}}{\frac{π}{3}}

Divide fractions:

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

= \frac{3 \cdot 3}{2 π}

= \frac{3 3}{2 π}

cos (arctan (\frac{12}{5})) - (arcsin (- \frac{3}{5}))

sin (22 5^{\circ}) + cos (- 13 5^{\circ})

arccos (\frac{3}{6})

cos (8.1)

- sin ((\frac{π}{2})^{2}) \cdot 2 (\frac{π}{2})

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