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

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

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2cos(pi/6)+sin(pi/3)

2 cos (\frac{π}{6}) + sin (\frac{π}{3})

3 + \frac{3}{2}

Decimal Notation

2.59807 \dots

Solution steps

2 cos (\frac{π}{6}) + sin (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{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{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

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

Simplify

2 \cdot \frac{3}{2} + \frac{3}{2} : 3 + \frac{3}{2}

2 \cdot \frac{3}{2} + \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

= 3 + \frac{3}{2}

= 3 + \frac{3}{2}

arctan (\frac{10}{25})

\frac{117}{tan ( 3 )}

arccos (\frac{- 2}{14 26})

sin (2 arctan (- \frac{3}{4}))

arctan (\frac{- 13.79}{25.54})

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