What is the value of (4(sin(45)))/3 ?

The value of (4(sin(45)))/3 is (2sqrt(2))/3

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(4(sin(45)))/3

\frac{4 ( sin ( 4 5 ^{\circ} ) )}{3}

\frac{2 2}{3}

Decimal Notation

0.94280 \dots

Solution steps

\frac{4 ( sin ( 4 5 ^{\circ} ) )}{3}

= \frac{4 sin ( 4 5 ^{\circ} )}{3}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

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

Simplify

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

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

Multiply

4 \cdot \frac{2}{2} : 22

4 \cdot \frac{2}{2}

Multiply fractions:

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

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

Divide the numbers:

\frac{4}{2} = 2

= 22

= \frac{2 2}{3}

= \frac{2 2}{3}

arctan (0.71)

arcsin (cos (\frac{π}{7}))

sec (- 66 0^{\circ})

arctan (\frac{14}{29})

1 - sin (π)

What is the value of (4(sin(45)))/3 ?
The value of (4(sin(45)))/3 is (2sqrt(2))/3