What is the value of (8sin(45))/7 ?

The value of (8sin(45))/7 is (4sqrt(2))/7

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(8sin(45))/7

\frac{8 sin ( 4 5 ^{\circ} )}{7}

\frac{4 2}{7}

Decimal Notation

0.80812 \dots

Solution steps

\frac{8 sin ( 4 5 ^{\circ} )}{7}

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{8 \cdot \frac{2}{2}}{7}

Simplify

\frac{8 \cdot \frac{2}{2}}{7} : \frac{4 2}{7}

\frac{8 \cdot \frac{2}{2}}{7}

Multiply

8 \cdot \frac{2}{2} : 42

8 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 8}{2}

Divide the numbers:

\frac{8}{2} = 4

= 42

= \frac{4 2}{7}

= \frac{4 2}{7}

2 - 2 cosh (0.1 - 2)

sin (0.0476)

1.758 + \frac{sin ( 4 )}{4} (3.9 - 4)

arctan (2) \cdot 2

sin (π) + cos (0) + tan (\frac{3 π}{4})