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

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

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2sin(-pi/3)cos(-pi/3)

2 sin (- \frac{π}{3}) cos (- \frac{π}{3})

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

2 sin (- \frac{π}{3}) cos (- \frac{π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{3}) = cos (\frac{π}{3})

= 2 sin (- \frac{π}{3}) cos (\frac{π}{3})

Use the following property:

sin (- x) = - sin (x)

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

= 2 (- sin (\frac{π}{3})) cos (\frac{π}{3})

Simplify

= - 2 sin (\frac{π}{3}) cos (\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}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

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

Simplify

- 2 \cdot \frac{3}{2} \cdot \frac{1}{2} : - \frac{3}{2}

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

Multiply fractions:

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

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

Cancel the common factor:

2

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

Multiply:

3 \cdot 1 = 3

= - \frac{3}{2}

= - \frac{3}{2}

csch (0)

cos (100 π)

cos (40 0^{\circ}) sec (4 0^{\circ})

10 sin (5 0^{\circ})

csc (\frac{- 11 π}{6})

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