What is the value of 2sin(150)cos(150) ?

The value of 2sin(150)cos(150) is -(sqrt(3))/2

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2sin(150)cos(150)

2 sin (15 0^{\circ}) cos (15 0^{\circ})

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

2 sin (15 0^{\circ}) cos (15 0^{\circ})

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

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

Simplify

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

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

Remove parentheses:

(- a) = - a

= - 2 \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 2}{2 \cdot 2}

Cancel the common factor:

2

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

Multiply:

1 \cdot 3 = 3

= - \frac{3}{2}

= - \frac{3}{2}

cos (0.45)

arctan (tan (4 5^{\circ}))

\frac{- 0.5}{sin ( - 0.5 )}

sec (5 3^{\circ})

\frac{98}{cos ( 3 1 ^{\circ} )}

What is the value of 2sin(150)cos(150) ?
The value of 2sin(150)cos(150) is -(sqrt(3))/2