What is the value of 6.1cos(60) ?

The value of 6.1cos(60) is 61/20

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6.1cos(60)

6.1 cos (6 0^{\circ})

\frac{61}{20}

Decimal

3.05

Solution steps

6.1 cos (6 0^{\circ})

= \frac{61}{10} 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}

= \frac{61}{10} \cdot \frac{1}{2}

Simplify

\frac{61}{10} \cdot \frac{1}{2} : \frac{61}{20}

\frac{61}{10} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{61 \cdot 1}{10 \cdot 2}

Multiply the numbers:

61 \cdot 1 = 61

= \frac{61}{10 \cdot 2}

Multiply the numbers:

10 \cdot 2 = 20

= \frac{61}{20}

= \frac{61}{20}