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Popular Trigonometria >

((6)^2sin^2(30))/(9.8)

Solução

\frac{( 6 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{9.8}

Solução

\frac{45}{49}

+1

Decimal

0.91836 \dots

Passos da solução

\frac{( 6 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{9.8}

= \frac{6 ^{2} sin ^{2} ( 3 0 ^{\circ} )}{\frac{49}{5}}

Utilizar a seguinte identidade trivial:

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

sin (3 0^{\circ})

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

:

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{6 ^{2} ( \frac{1}{2} ) ^{2}}{\frac{49}{5}}

Simplificar

\frac{6 ^{2} ( \frac{1}{2} ) ^{2}}{\frac{49}{5}} : \frac{45}{49}

\frac{6 ^{2} ( \frac{1}{2} ) ^{2}}{\frac{49}{5}}

Aplicar as propriedades das frações:

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

= \frac{6 ^{2} ( \frac{1}{2} ) ^{2} \cdot 5}{49}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

Aplicar as propriedades dos expoentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Aplicar a regra

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

= \frac{6 ^{2} \cdot 5 \cdot \frac{1}{2 ^{2}}}{49}

Multiplicar

6^{2} \cdot \frac{1}{2 ^{2}} \cdot 5 : 45

6^{2} \cdot \frac{1}{2 ^{2}} \cdot 5

Multiplicar frações:

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

= \frac{1 \cdot 6 ^{2} \cdot 5}{2 ^{2}}

Multiplicar os números:

1 \cdot 5 = 5

= \frac{6 ^{2} \cdot 5}{2 ^{2}}

Fatorar

6^{2} : 2^{2} \cdot 3^{2}

Fatorar

6 = 2 \cdot 3

= (2 \cdot 3)^{2}

Aplicar as propriedades dos expoentes:

(ab)^{c} = a^{c} b^{c}

= 2^{2} \cdot 3^{2}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5}{2 ^{2}}

Eliminar o fator comum:

2^{2}

= 3^{2} \cdot 5

3^{2} = 9

= 9 \cdot 5

Multiplicar os números:

9 \cdot 5 = 45

= 45

= \frac{45}{49}

= \frac{45}{49}

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