What is the value of -2cos(pi/6) ?

The value of -2cos(pi/6) is -sqrt(3)

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-2cos(pi/6)

- 2 cos (\frac{π}{6})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

- 2 cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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}

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

Simplify

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

- 2 \cdot \frac{3}{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 (\frac{- 5 π}{4})

sin (arccos (\frac{12}{13}))

\frac{sin ( 2 )}{2}

arcsin (0.43)

csc (- 6 0^{\circ})