What is the value of 4sin(pi/4)cos(pi/6) ?

The value of 4sin(pi/4)cos(pi/6) is square root of 6

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4sin(pi/4)cos(pi/6)

4 sin (\frac{π}{4}) cos (\frac{π}{6})

6

Decimal Notation

2.44948 \dots

Solution steps

4 sin (\frac{π}{4}) cos (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 4 \cdot \frac{2}{2} \cdot \frac{3}{2}

Simplify

4 \cdot \frac{2}{2} \cdot \frac{3}{2} : 6

4 \cdot \frac{2}{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{2 3 \cdot 4}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 2 3}{4}

Divide the numbers:

\frac{4}{4} = 1

= 23

Apply radical rule:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= 6

arcsin (\frac{20}{25})

[2 (cos (\frac{π}{4}) + i sin (\frac{π}{4}))]^{6}

sin (8.6)

sin (23 3^{\circ})

2 sin (\frac{π}{5}) cos (\frac{π}{5})

What is the value of 4sin(pi/4)cos(pi/6) ?
The value of 4sin(pi/4)cos(pi/6) is square root of 6