What is the value of 1000cos(30) ?

The value of 1000cos(30) is 500sqrt(3)

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1000cos(30)

1000 cos (3 0^{\circ})

5003

Decimal Notation

866.02540 \dots

Solution steps

1000 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}

= 1000 \cdot \frac{3}{2}

Simplify

1000 \cdot \frac{3}{2} : 5003

1000 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 1000}{2}

Divide the numbers:

\frac{1000}{2} = 500

= 5003

= 5003

cot (\frac{π}{9})

2 cos (\frac{π}{2}) + sin (2 (\frac{π}{2}))

300 \cdot cos (5 5^{\circ}) \cdot 42

20 cos (5 5^{\circ})

sec (arcsin (\frac{2 5}{5}))