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

The value of sqrt(3)(pi/3)+2cos(pi/3) is (sqrt(3)pi)/3+1

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sqrt(3)(pi/3)+2cos(pi/3)

3 (\frac{π}{3}) + 2 cos (\frac{π}{3})

\frac{3 π}{3} + 1

Decimal Notation

2.81379 \dots

Solution steps

3 (\frac{π}{3}) + 2 cos (\frac{π}{3})

= 3 \frac{π}{3} + 2 cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

= 3 \frac{π}{3} + 2 \cdot \frac{1}{2}

Simplify

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

3 \frac{π}{3} + 2 \cdot \frac{1}{2}

3 \frac{π}{3} = \frac{3 π}{3}

3 \frac{π}{3}

Multiply fractions:

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

= \frac{π 3}{3}

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

2 \cdot \frac{1}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= \frac{3 π}{3} + 1

= \frac{3 π}{3} + 1

0.71 (9.8) sin (1 0^{\circ})

sin (\frac{5}{10})

1 - cos (\frac{5 π}{3})

1 \cdot sin (1) - 1

sec^{2} (π) - 9 sin (π)

What is the value of sqrt(3)(pi/3)+2cos(pi/3) ?
The value of sqrt(3)(pi/3)+2cos(pi/3) is (sqrt(3)pi)/3+1