What is the value of 2sqrt(3)*cos(60) ?

The value of 2sqrt(3)*cos(60) is square root of 3

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2sqrt(3)*cos(60)

23 \cdot cos (6 0^{\circ})

3

Decimal

1.73205 \dots

Solution steps

23 cos (6 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}

= 23 \frac{1}{2}

Simplify

23 \frac{1}{2} : 3

23 \frac{1}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 1 \cdot 3

Multiply:

1 \cdot 3 = 3

= 3

= 3

What is the value of 2sqrt(3)*cos(60) ?
The value of 2sqrt(3)*cos(60) is square root of 3