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}

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}

Use the following trivial identity:

cos (\frac{π}{3}) = \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}

= - \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