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

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

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2cos((5pi)/6)+sin(2((5pi)/6))

2 cos (\frac{5 π}{6}) + sin (2 (\frac{5 π}{6}))

- 3 - \frac{3}{2}

Decimal Notation

- 2.59807 \dots

Solution steps

2 cos (\frac{5 π}{6}) + sin (2 (\frac{5 π}{6}))

= 2 cos (\frac{5 π}{6}) + sin (2 \cdot \frac{5 π}{6})

Rewrite using trig identities:

sin (2 \cdot \frac{5 π}{6}) = 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

sin (2 \cdot \frac{5 π}{6})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

= 2 cos (\frac{5 π}{6}) + 2 sin (\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}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (\frac{5 π}{6})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= 2 (- \frac{3}{2}) + 2 \cdot \frac{1}{2} (- \frac{3}{2})

Simplify

2 (- \frac{3}{2}) + 2 \cdot \frac{1}{2} (- \frac{3}{2}) : - 3 - \frac{3}{2}

2 (- \frac{3}{2}) + 2 \cdot \frac{1}{2} (- \frac{3}{2})

Remove parentheses:

(- a) = - a

= - 2 \cdot \frac{3}{2} - 2 \cdot \frac{1}{2} \cdot \frac{3}{2}

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

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

2 \cdot \frac{1}{2} \cdot \frac{3}{2} = \frac{3}{2}

2 \cdot \frac{1}{2} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{1 \cdot 3 \cdot 2}{2 \cdot 2}

Cancel the common factor:

2

= \frac{1 \cdot 3}{2}

Multiply:

1 \cdot 3 = 3

= \frac{3}{2}

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

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

\frac{1 - cos ( 3 ( 0.999 ) - 3 )}{5 ( ( 0.999 ) - 1 ) ^{2}}

sin (6 0^{\circ}) - sin (3 0^{\circ})

- \frac{1}{4} sin (2 π)

14 sin (3 5^{\circ})

8 cos (\frac{7 π}{6})

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