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

The value of sin(pi/(12))cos(pi/(12)) is 1/4

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sin(pi/(12))cos(pi/(12))

sin (\frac{π}{12}) cos (\frac{π}{12})

\frac{1}{4}

Decimal Notation

0.25

Solution steps

sin (\frac{π}{12}) cos (\frac{π}{12})

Rewrite using trig identities:

\frac{sin ( \frac{π}{6} )}{2}

sin (\frac{π}{12}) cos (\frac{π}{12})

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= \frac{sin ( 2 \cdot \frac{π}{12} )}{2}

Simplify:

2 \cdot \frac{π}{12} = \frac{π}{6}

2 \cdot \frac{π}{12}

Multiply fractions:

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

= \frac{π 2}{12}

Cancel the common factor:

2

= \frac{π}{6}

= \frac{sin ( \frac{π}{6} )}{2}

= \frac{sin ( \frac{π}{6} )}{2}

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{\frac{1}{2}}{2}

Simplify

\frac{\frac{1}{2}}{2} : \frac{1}{4}

\frac{\frac{1}{2}}{2}

Apply the fraction rule:

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

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= \frac{1}{4}

arctan (50)

arcsin (sin (\frac{π}{5}))

arctan (13)

tan (2 arcsin (\frac{4}{5}))

arcsin (\frac{5}{12})

What is the value of sin(pi/(12))cos(pi/(12)) ?
The value of sin(pi/(12))cos(pi/(12)) is 1/4