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

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

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5cos((5pi)/6)

5 cos (\frac{5 π}{6})

- \frac{5 3}{2}

Decimal Notation

- 4.33012 \dots

Solution steps

5 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}

= 5 (- \frac{3}{2})

Simplify

5 (- \frac{3}{2}) : - \frac{5 3}{2}

5 (- \frac{3}{2})

Remove parentheses:

(- a) = - a

= - 5 \cdot \frac{3}{2}

Multiply fractions:

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

= - \frac{3 \cdot 5}{2}

= - \frac{5 3}{2}

- \frac{- 10 - 16}{2} sin (- 6 0^{\circ}) + (- 5) cos (- 6 0^{\circ})

sin (2.4)

200 \cdot cos (12 0^{\circ})

arctan (- \frac{π}{36})

150 \cdot cos (1 0^{\circ})

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