What is the value of (100^2(2sin(30)))/(9.8)-999.984741 ?

The value of (100^2(2sin(30)))/(9.8)-999.984741 is 50000/49-999.984741

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(100^2(2sin(30)))/(9.8)-999.984741

\frac{10 0 ^{2} ( 2 sin ( 3 0 ^{\circ} ) )}{9.8} - 999.984741

\frac{50000}{49} - 999.984741

Decimal Notation

20.42342 \dots

Solution steps

\frac{10 0 ^{2} ( 2 sin ( 3 0 ^{\circ} ) )}{9.8} - 999.984741

= \frac{10 0 ^{2} \cdot 2 sin ( 3 0 ^{\circ} )}{\frac{49}{5}} - 999.984741

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\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{1}{2}

= \frac{10 0 ^{2} \cdot 2 \cdot \frac{1}{2}}{\frac{49}{5}} - 999.984741

Simplify

\frac{10 0 ^{2} \cdot 2 \cdot \frac{1}{2}}{\frac{49}{5}} - 999.984741 : \frac{50000}{49} - 999.984741

\frac{10 0 ^{2} \cdot 2 \cdot \frac{1}{2}}{\frac{49}{5}} - 999.984741

\frac{10 0 ^{2} \cdot 2 \cdot \frac{1}{2}}{\frac{49}{5}} = \frac{10 0 ^{2} \cdot 10 \cdot \frac{1}{2}}{49}

\frac{10 0 ^{2} \cdot 2 \cdot \frac{1}{2}}{\frac{49}{5}}

Apply the fraction rule:

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

= \frac{10 0 ^{2} \cdot 2 \cdot \frac{1}{2} \cdot 5}{49}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{10 0 ^{2} \cdot 10 \cdot \frac{1}{2}}{49}

= \frac{10 0 ^{2} \cdot 10 \cdot \frac{1}{2}}{49} - 999.984741

\frac{10 \cdot 10 0 ^{2} \cdot \frac{1}{2}}{49} = \frac{50000}{49}

\frac{10 \cdot 10 0 ^{2} \cdot \frac{1}{2}}{49}

10 \cdot 10 0^{2} \cdot \frac{1}{2} = 100000 \cdot \frac{1}{2}

10 \cdot 10 0^{2} \cdot \frac{1}{2}

10 0^{2} = 10000

= 10 \cdot 10000 \cdot \frac{1}{2}

Multiply the numbers:

10 \cdot 10000 = 100000

= 100000 \cdot \frac{1}{2}

= \frac{100000 \cdot \frac{1}{2}}{49}

Multiply

100000 \cdot \frac{1}{2} : 50000

100000 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 100000}{2}

Multiply the numbers:

1 \cdot 100000 = 100000

= \frac{100000}{2}

Divide the numbers:

\frac{100000}{2} = 50000

= 50000

= \frac{50000}{49}

= \frac{50000}{49} - 999.984741

= \frac{50000}{49} - 999.984741

\frac{sin ( 8 0 ^{\circ} ) + sin ( 2 0 ^{\circ} )}{cos ( 8 0 ^{\circ} ) + cos ( 2 0 ^{\circ} )}

8 cos (\frac{π}{2} + 0.1)

ln (2 + tan (\frac{3 π}{32}))

sin (\frac{1}{( \frac{2}{9 π} )})

3 sin (24 0^{\circ})

What is the value of (100^2(2sin(30)))/(9.8)-999.984741 ?
The value of (100^2(2sin(30)))/(9.8)-999.984741 is 50000/49-999.984741