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32.09(1+0.0053sin^2(45))

Solución

32.09 (1 + 0.0053 sin^{2} (4 5^{\circ}))

\frac{64350077}{2000000}

Notación decimal

32.1750385

Pasos de solución

32.09 (1 + 0.0053 sin^{2} (4 5^{\circ}))

= \frac{3209}{100} (1 + \frac{53}{10000} sin^{2} (4 5^{\circ}))

Utilizar la siguiente identidad trivial:

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

sin (4 5^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

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{3209}{100} 1 + \frac{53}{10000} (\frac{2}{2})^{2}

Simplificar

\frac{3209}{100} 1 + \frac{53}{10000} (\frac{2}{2})^{2} : \frac{64350077}{2000000}

\frac{3209}{100} 1 + \frac{53}{10000} (\frac{2}{2})^{2}

\frac{53}{10000} (\frac{2}{2})^{2} = \frac{53}{20000}

\frac{53}{10000} (\frac{2}{2})^{2}

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

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

Aplicar las leyes de los exponentes:

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

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

(2)^{2} : 2

Aplicar las leyes de los exponentes:

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

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

Aplicar las leyes de los exponentes:

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

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

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

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

2

= 1

= 2

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

Eliminar los terminos comunes:

2

= \frac{1}{2}

= \frac{1}{2} \cdot \frac{53}{10000}

Multiplicar fracciones:

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

= \frac{53 \cdot 1}{10000 \cdot 2}

Multiplicar los numeros:

53 \cdot 1 = 53

= \frac{53}{10000 \cdot 2}

Multiplicar los numeros:

10000 \cdot 2 = 20000

= \frac{53}{20000}

= \frac{3209}{100} (\frac{53}{20000} + 1)

Simplificar

1 + \frac{53}{20000}

en una fracción:

\frac{20053}{20000}

1 + \frac{53}{20000}

Convertir a fracción:

1 = \frac{1 \cdot 20000}{20000}

= \frac{1 \cdot 20000}{20000} + \frac{53}{20000}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot 20000 + 53}{20000}

1 \cdot 20000 + 53 = 20053

1 \cdot 20000 + 53

Multiplicar los numeros:

1 \cdot 20000 = 20000

= 20000 + 53

Sumar:

20000 + 53 = 20053

= 20053

= \frac{20053}{20000}

= \frac{3209}{100} \cdot \frac{20053}{20000}

Multiplicar fracciones:

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

= \frac{3209 \cdot 20053}{100 \cdot 20000}

Multiplicar los numeros:

3209 \cdot 20053 = 64350077

= \frac{64350077}{100 \cdot 20000}

Multiplicar los numeros:

100 \cdot 20000 = 2000000

= \frac{64350077}{2000000}

= \frac{64350077}{2000000}

arctan (tan (- \frac{π}{7}))

arctan (\frac{6.1}{4})

2 - cos (π)

arctan (\frac{1.6 sin ( 4 0 ^{\circ} )}{1.6 + 1.6 cos ( 4 0 ^{\circ} )})

cos (3 6^{\circ}) - sin (1 8^{\circ})