What is the value of 2cos(60)sin(30) ?

The value of 2cos(60)sin(30) is 1/2

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2cos(60)sin(30)

2 cos (6 0^{\circ}) sin (3 0^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

2 cos (6 0^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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{1}{2}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

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

Simplify

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

2 \cdot \frac{1}{2} \cdot \frac{1}{2}

Convert element to fraction:

2 = \frac{2}{1}

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

Multiply fractions:

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

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

Cancel the common factor:

2

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

Cancel the common factor:

1

= \frac{1}{2}

= \frac{1}{2}

\frac{1}{cos ( \frac{1}{4} )}

9 cos (1 2^{\circ})

cos (- 20 0^{\circ})

arctan (\frac{56}{91})

8 \cdot (\frac{2 0 ^{2}}{4 tan ( \frac{45}{2} )})