What is the value of cos(45)*600 ?

The value of cos(45)*600 is 300sqrt(2)

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cos(45)*600

cos (4 5^{\circ}) \cdot 600

3002

Decimal

424.26406 \dots

Solution steps

cos (4 5^{\circ}) \cdot 600

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

= \frac{2}{2} \cdot 600

Simplify

\frac{2}{2} \cdot 600 : 3002

\frac{2}{2} \cdot 600

Multiply fractions:

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

= \frac{2 \cdot 600}{2}

Divide the numbers:

\frac{600}{2} = 300

= 3002

= 3002