What is the value of 1000cos(60) ?

The value of 1000cos(60) is 500

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1000cos(60)

1000 cos (6 0^{\circ})

500

Solution steps

1000 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}

= 1000 \cdot \frac{1}{2}

Simplify

1000 \cdot \frac{1}{2} : 500

1000 \cdot \frac{1}{2}

Convert element to fraction:

1000 = \frac{1000}{1}

= \frac{1}{2} \cdot \frac{1000}{1}

Cross-cancel common factor:

2

= \frac{500}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 500

= 500

sin (arccos (\frac{5}{13}) - arccos (\frac{4}{5}))

π sin (2 π)

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

sin (2 arctan (2))

\frac{tan ( 7 2 ^{\circ} ) - tan ( 1 2 ^{\circ} )}{1 + tan ( 7 2 ^{\circ} ) tan ( 1 2 ^{\circ} )}