What is the value of cos(30)*2 ?

The value of cos(30)*2 is square root of 3

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cos(30)*2

cos (3 0^{\circ}) \cdot 2

3

Decimal Notation

1.73205 \dots

Solution steps

cos (3 0^{\circ}) \cdot 2

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}

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

Simplify

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

\frac{3}{2} \cdot 2

Multiply fractions:

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

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

Cancel the common factor:

2

= 3

= 3

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

sin^{2} (3 2^{\circ})

\frac{300}{sin ( 6 0 ^{\circ} )}

arctan (\frac{40}{25})

tan (arcsin (- \frac{12}{13}))