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

The value of 2cos(pi/6)+sin((5pi)/6)-tan(pi/3) is 1/2

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2cos(pi/6)+sin((5pi)/6)-tan(pi/3)

2 cos (\frac{π}{6}) + sin (\frac{5 π}{6}) - tan (\frac{π}{3})

\frac{1}{2}

Decimal

0.5

Solution steps

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

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

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

Simplify

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

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

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{1}{2} - 3

Group like terms

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

Add similar elements:

3 - 3 = 0

= \frac{1}{2}

= \frac{1}{2}

What is the value of 2cos(pi/6)+sin((5pi)/6)-tan(pi/3) ?
The value of 2cos(pi/6)+sin((5pi)/6)-tan(pi/3) is 1/2