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

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

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-2cos((5pi)/6)

- 2 cos (\frac{5 π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

- 2 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}

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

Simplify

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

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

Apply rule

- (- a) = a

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 3

= 3

sec (\frac{- 2 π}{3})

8 cos (4 0^{\circ})

7 cos (5 0^{\circ})

sin (5 \frac{π}{2})

sin (- 2 5^{\circ})

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