What is the value of 5*9.81*cos(30) ?

The value of 5*9.81*cos(30) is (981sqrt(3))/(40)

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59.81cos(30)

5 \cdot 9.81 \cdot cos (3 0^{\circ})

\frac{981 3}{40}

Decimal

42.47854 \dots

Solution steps

5 \cdot 9.81 cos (3 0^{\circ})

= 5 \cdot \frac{981}{100} 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}

= 5 \cdot \frac{981}{100} \cdot \frac{3}{2}

Simplify

5 \cdot \frac{981}{100} \cdot \frac{3}{2} : \frac{981 3}{40}

5 \cdot \frac{981}{100} \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{981 3 \cdot 5}{100 \cdot 2}

Multiply the numbers:

981 \cdot 5 = 4905

= \frac{4905 3}{100 \cdot 2}

Multiply the numbers:

100 \cdot 2 = 200

= \frac{4905 3}{200}

Cancel the common factor:

5

= \frac{981 3}{40}

= \frac{981 3}{40}

What is the value of 5*9.81*cos(30) ?
The value of 5*9.81*cos(30) is (981sqrt(3))/(40)