What is the value of 80*20*cos(30) ?

The value of 80*20*cos(30) is 800sqrt(3)

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8020cos(30)

80 \cdot 20 \cdot cos (3 0^{\circ})

8003

Decimal

1385.64064 \dots

Solution steps

80 \cdot 20 cos (3 0^{\circ})

Use the following trivial identity:

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

cos (3 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}

= 80 \cdot 20 \cdot \frac{3}{2}

Simplify

80 \cdot 20 \cdot \frac{3}{2} : 8003

80 \cdot 20 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 80 \cdot 20}{2}

Multiply the numbers:

80 \cdot 20 = 1600

= \frac{1600 3}{2}

Divide the numbers:

\frac{1600}{2} = 800

= 8003

= 8003