What is the value of 4.5*(2pi)/3*sin(pi-pi/2) ?

The value of 4.5*(2pi)/3*sin(pi-pi/2) is 3pi

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4.5(2pi)/3sin(pi-pi/2)

4.5 \cdot \frac{2 π}{3} \cdot sin (π - \frac{π}{2})

3 π

Decimal Notation

9.42477 \dots

Solution steps

4.5 \cdot \frac{2 π}{3} sin (π - \frac{π}{2})

= \frac{9}{2} \cdot \frac{2 π}{3} sin (π - \frac{π}{2})

Rewrite using trig identities:

sin (π - \frac{π}{2}) = 1

sin (π - \frac{π}{2})

Simplify:

π - \frac{π}{2} = \frac{π}{2}

π - \frac{π}{2}

Convert element to fraction:

π = \frac{π 2}{2}

= \frac{π 2}{2} - \frac{π}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{π 2 - π}{2}

Add similar elements:

2 π - π = π

= \frac{π}{2}

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 1

= \frac{9}{2} \cdot \frac{2 π}{3} \cdot 1

Simplify

\frac{9}{2} \cdot \frac{2 π}{3} \cdot 1 : 3 π

\frac{9}{2} \cdot \frac{2 π}{3} \cdot 1

Multiply fractions:

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

= 1 \cdot \frac{9 \cdot 2 π}{2 \cdot 3}

Cancel the common factor:

2

= 1 \cdot \frac{9 π}{3}

Divide the numbers:

\frac{9}{3} = 3

= 1 \cdot 3 π

Multiply the numbers:

1 \cdot 3 = 3

= 3 π

= 3 π

\frac{9}{sin ( 7 0 ^{\circ} )}

- 10 cos (23 0^{\circ})

100 sin (5)

cos (3 0^{\circ}) 6

\frac{sin ( 3 \frac{π}{2} )}{3}

What is the value of 4.5*(2pi)/3*sin(pi-pi/2) ?
The value of 4.5*(2pi)/3*sin(pi-pi/2) is 3pi