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

The value of 2sin(pi/3)-3tan(pi/6) is 0

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2sin(pi/3)-3tan(pi/6)

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

0

Solution steps

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

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}

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

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}

= \frac{3}{3}

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

Simplify

2 \cdot \frac{3}{2} - 3 \cdot \frac{3}{3} : 0

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

3 \cdot \frac{3}{3}

Multiply fractions:

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

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

Cancel the common factor:

3

= 3

= 3 - 3

Add similar elements:

3 - 3 = 0

= 0

= 0

cos (10 5^{\circ}) sin (1 5^{\circ})

40 \cdot cos (6 0^{\circ})

5 sin (\frac{π}{6})

arccos (2 π)

arccos (cos (\frac{6 π}{5}))

What is the value of 2sin(pi/3)-3tan(pi/6) ?
The value of 2sin(pi/3)-3tan(pi/6) is 0