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

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

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-2sin(pi/3)+pi/3

- 2 sin (\frac{π}{3}) + \frac{π}{3}

- 3 + \frac{π}{3}

Decimal Notation

- 0.68485 \dots

Solution steps

- 2 sin (\frac{π}{3}) + \frac{π}{3}

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{π}{3}

Simplify

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

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

= - 3 + \frac{π}{3}

2 - cos (2)

2 arccos (\frac{4}{5})

cos (\frac{25}{24})

cos (\frac{( - 5 \cdot π )}{3})

arctan (0.675)

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