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

The value of 2(pi/3)sin(pi/3)+cos(pi/3)(pi/3)^2 is (sqrt(3)pi)/3+(pi^2)/(18)

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

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

\frac{3 π}{3} + \frac{π ^{2}}{18}

Decimal Notation

2.36211 \dots

Solution steps

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

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

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}

= 2 \cdot \frac{π}{3} \cdot \frac{3}{2} + \frac{1}{2} (\frac{π}{3})^{2}

Simplify

2 \cdot \frac{π}{3} \cdot \frac{3}{2} + \frac{1}{2} (\frac{π}{3})^{2} : \frac{3 π}{3} + \frac{π ^{2}}{18}

2 \cdot \frac{π}{3} \cdot \frac{3}{2} + \frac{1}{2} (\frac{π}{3})^{2}

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

2 \cdot \frac{π}{3} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{π 3 \cdot 2}{3 \cdot 2}

Cancel the common factor:

2

= \frac{π 3}{3}

\frac{1}{2} (\frac{π}{3})^{2} = \frac{π ^{2}}{18}

\frac{1}{2} (\frac{π}{3})^{2}

(\frac{π}{3})^{2} = \frac{π ^{2}}{3 ^{2}}

(\frac{π}{3})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{π ^{2}}{3 ^{2}}

= \frac{1}{2} \cdot \frac{π ^{2}}{3 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot π ^{2}}{2 \cdot 3 ^{2}}

Multiply:

1 \cdot π^{2} = π^{2}

= \frac{π ^{2}}{3 ^{2} \cdot 2}

2 \cdot 3^{2} = 18

2 \cdot 3^{2}

3^{2} = 9

= 2 \cdot 9

Multiply the numbers:

2 \cdot 9 = 18

= 18

= \frac{π ^{2}}{18}

= \frac{3 π}{3} + \frac{π ^{2}}{18}

= \frac{3 π}{3} + \frac{π ^{2}}{18}

2 (3 0^{\circ}) cos^{2} (3 0^{\circ})

2 - 2 sin (2)

tan (- 60 0^{\circ})

\frac{1}{4} sin (4 π)

e^{π - π} tan (29 π)

What is the value of 2(pi/3)sin(pi/3)+cos(pi/3)(pi/3)^2 ?
The value of 2(pi/3)sin(pi/3)+cos(pi/3)(pi/3)^2 is (sqrt(3)pi)/3+(pi^2)/(18)