What is the value of 1+2cos((2pi)/3) ?

The value of 1+2cos((2pi)/3) is 0

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1+2cos((2pi)/3)

1 + 2 cos (\frac{2 π}{3})

0

Solution steps

1 + 2 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}

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

Simplify

1 + 2 (- \frac{1}{2}) : 0

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

Remove parentheses:

(- a) = - a

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

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

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 - 1

Subtract the numbers:

1 - 1 = 0

= 0

= 0

\frac{cos ( 13 5 ^{\circ} )}{tan ( 22 5 ^{\circ} )}

50 (3 + 3 cos (5 3^{\circ}))

\frac{cos ( π )}{12}

cos (5.8)

arctan (\frac{- 16}{0})