What is the value of cos(8/3 pi) ?

The value of cos(8/3 pi) is -1/2

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cos(8/3 pi)

cos (\frac{8}{3} π)

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (\frac{8}{3} π)

Simplify:

\frac{8}{3} π = \frac{8 π}{3}

\frac{8}{3} π

Multiply fractions:

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

= \frac{8 π}{3}

= cos (\frac{8 π}{3})

cos (\frac{8 π}{3}) = cos (\frac{2 π}{3})

cos (\frac{8 π}{3})

Rewrite

\frac{8 π}{3}

2 π + \frac{2 π}{3}

= cos (2 π + \frac{2 π}{3})

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

cos (2 π + \frac{2 π}{3}) = cos (\frac{2 π}{3})

= cos (\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}

cos (35.8899 4^{\circ})

128 + 127.5 sin (\frac{2 π}{16} \cdot 13)

128 + 127.5 sin (\frac{2 π}{16} \cdot 11)

178.09 sin (6 5^{\circ})

128 + 127.5 sin (\frac{2 π}{16} \cdot 12)