What is the value of -4cos((2pi)/3) ?

The value of -4cos((2pi)/3) is 2

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-4cos((2pi)/3)

- 4 cos (\frac{2 π}{3})

2

Solution steps

- 4 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}

= - 4 (- \frac{1}{2})

Simplify

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

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

Apply rule

- (- a) = a

= 4 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 4}{2}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= 2

sin (\frac{7}{2} π)

cos (2 arccos (\frac{1}{3}))

3 sin (3 7^{\circ})

arcsin (cos (\frac{3 π}{5}))

csc (- \frac{π}{12})