What is the value of cos(3((2pi)/9)) ?

The value of cos(3((2pi)/9)) is -1/2

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cos(3((2pi)/9))

cos (3 (\frac{2 π}{9}))

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (3 (\frac{2 π}{9}))

= cos (3 \cdot \frac{2 π}{9})

Simplify:

3 \cdot \frac{2 π}{9} = \frac{2 π}{3}

3 \cdot \frac{2 π}{9}

Multiply fractions:

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

= \frac{2 π 3}{9}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{6 π}{9}

Cancel the common factor:

3

= \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}

arctan (\frac{6}{16})

csc^{2} (\frac{5 π}{6})

arctan (\frac{- 5}{1})

\frac{180}{tan ( 1 8 ^{\circ} )} + 240

25 cos (- 4 5^{\circ})