What is the value of 5sin(pi/6)sin(pi/3) ?

The value of 5sin(pi/6)sin(pi/3) is (5sqrt(3))/4

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5sin(pi/6)sin(pi/3)

5 sin (\frac{π}{6}) sin (\frac{π}{3})

\frac{5 3}{4}

Decimal Notation

2.16506 \dots

Solution steps

5 sin (\frac{π}{6}) sin (\frac{π}{3})

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}

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}

= 5 \cdot \frac{1}{2} \cdot \frac{3}{2}

Simplify

5 \cdot \frac{1}{2} \cdot \frac{3}{2} : \frac{5 3}{4}

5 \cdot \frac{1}{2} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{1 \cdot 3 \cdot 5}{2 \cdot 2}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5 3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{5 3}{4}

= \frac{5 3}{4}

arctan (\frac{43}{45})

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

1 - arctan (1)

sin (\frac{9}{4})

cos (10 5^{\circ}) cos (7 5^{\circ})

What is the value of 5sin(pi/6)sin(pi/3) ?
The value of 5sin(pi/6)sin(pi/3) is (5sqrt(3))/4