What is the value of 2cos((4pi)/6) ?

The value of 2cos((4pi)/6) is -1

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2cos((4pi)/6)

2 cos (\frac{4 π}{6})

- 1

Solution steps

2 cos (\frac{4 π}{6})

Rewrite using trig identities:

cos (\frac{4 π}{6}) = - \frac{1}{2}

cos (\frac{4 π}{6})

Simplify:

\frac{4 π}{6} = \frac{2 π}{3}

\frac{4 π}{6}

Cancel the common factor:

2

= \frac{2 π}{3}

= cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 π}{3})

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{1}{2}

= - \frac{1}{2}

= 2 (- \frac{1}{2})

Simplify

2 (- \frac{1}{2}) : - 1

2 (- \frac{1}{2})

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Cancel the common factor:

2

= - 1

= - 1

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