What is the value of (1)^2*sin(pi/3)*cos(pi/3) ?

The value of (1)^2*sin(pi/3)*cos(pi/3) is (sqrt(3))/4

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(1)^2sin(pi/3)cos(pi/3)

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

\frac{3}{4}

Decimal Notation

0.43301 \dots

Solution steps

(1)^{2} sin (\frac{π}{3}) cos (\frac{π}{3})

= 1^{2} sin (\frac{π}{3}) cos (\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}

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}

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

Simplify

1^{2} \cdot \frac{3}{2} \cdot \frac{1}{2} : \frac{3}{4}

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

Apply rule

1^{a} = 1

1^{2} = 1

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

Multiply fractions:

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

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

\frac{3 \cdot 1}{2 \cdot 2} = \frac{3}{4}

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

Multiply:

3 \cdot 1 = 3

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3}{4}

= 1 \cdot \frac{3}{4}

Multiply:

1 \cdot \frac{3}{4} = \frac{3}{4}

= \frac{3}{4}

= \frac{3}{4}

sin (arcsin (\frac{2 π}{3}))

\frac{π}{2} [sin (0) + sin (π)]

cos (arctan (\frac{5}{4}))

csc (- 39 0^{\circ})

2 (cos (9 0^{\circ}) + i sin (9 0^{\circ}))

What is the value of (1)^2*sin(pi/3)*cos(pi/3) ?
The value of (1)^2*sin(pi/3)*cos(pi/3) is (sqrt(3))/4