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

The value of 2(cos(2(pi/3))) is -1

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2(cos(2(pi/3)))

2 (cos (2 (\frac{π}{3})))

- 1

Solution steps

2 (cos (2 (\frac{π}{3})))

= 2 cos (2 \cdot \frac{π}{3})

Rewrite using trig identities:

cos (2 \cdot \frac{π}{3}) = - \frac{1}{2}

cos (2 \cdot \frac{π}{3})

Simplify:

2 \cdot \frac{π}{3} = \frac{2 π}{3}

2 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 2}{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

8 \cdot sin (3 5^{\circ})

2 \cdot arctan (2) - 5

arccos (- \frac{0.5}{1})

sin (1 0^{\circ}) sin (5 0^{\circ}) sin (7 0^{\circ})

4 cos (1) + 48 sin (1)