What is the value of (2(19.4)sin(45))/(9.8) ?

The value of (2(19.4)sin(45))/(9.8) is (97sqrt(2))/(49)

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(2(19.4)sin(45))/(9.8)

\frac{2 ( 19.4 ) sin ( 4 5 ^{\circ} )}{9.8}

\frac{97 2}{49}

Decimal Notation

2.79956 \dots

Solution steps

\frac{2 ( 19.4 ) sin ( 4 5 ^{\circ} )}{9.8}

= \frac{2 \cdot \frac{97}{5} sin ( 4 5 ^{\circ} )}{\frac{49}{5}}

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{2 \cdot \frac{97}{5} \cdot \frac{2}{2}}{\frac{49}{5}}

Simplify

\frac{2 \cdot \frac{97}{5} \cdot \frac{2}{2}}{\frac{49}{5}} : \frac{97 2}{49}

\frac{2 \cdot \frac{97}{5} \cdot \frac{2}{2}}{\frac{49}{5}}

Apply the fraction rule:

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

= \frac{2 \cdot \frac{97}{5} \cdot \frac{2}{2} \cdot 5}{49}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{10 \cdot \frac{97}{5} \cdot \frac{2}{2}}{49}

Multiply

10 \cdot \frac{97}{5} \cdot \frac{2}{2} : 972

10 \cdot \frac{97}{5} \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{97 2 \cdot 10}{5 \cdot 2}

Multiply the numbers:

97 \cdot 10 = 970

= \frac{970 2}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{970 2}{10}

Divide the numbers:

\frac{970}{10} = 97

= 972

= \frac{97 2}{49}

= \frac{97 2}{49}

7 sin (16 0^{\circ})

sec (\frac{7 π}{12})

10 \cdot cos (3 7^{\circ})

cos (\frac{23 π}{24}) sin (\frac{17 π}{24})

sin (2 arccos (\frac{1}{5}))

What is the value of (2(19.4)sin(45))/(9.8) ?
The value of (2(19.4)sin(45))/(9.8) is (97sqrt(2))/(49)