What is the value of cos(-5/6 pi) ?

The value of cos(-5/6 pi) is -(sqrt(3))/2

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cos(-5/6 pi)

cos (- \frac{5}{6} π)

- \frac{3}{2}

Decimal

- 0.86602 \dots

Solution steps

cos (- \frac{5}{6} π)

Simplify:

- \frac{5}{6} π = - \frac{5 π}{6}

- \frac{5}{6} π

Multiply fractions:

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

= - \frac{5 π}{6}

= cos (- \frac{5 π}{6})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{5 π}{6}) = cos (\frac{5 π}{6})

= cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 π}{6})

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{3}{2}

= - \frac{3}{2}