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solvefor θ,(90^2)/(250(32.2))=tan(θ)

Solución

resolver para

θ, \frac{9 0 ^{2}}{250 ( 32.2 )} = tan (θ)

Solución

θ = 0.78849 \dots + πn

+1

Grados

θ = 45.17738 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

\frac{9 0 ^{2}}{250 ( 32.2 )} = tan (θ)

Intercambiar lados

tan (θ) = \frac{9 0 ^{2}}{250 \cdot 32.2}

Simplificar

\frac{9 0 ^{2}}{250 \cdot 32.2} : \frac{162}{161}

\frac{9 0 ^{2}}{250 \cdot 32.2}

Multiplicar los numeros:

250 \cdot 32.2 = 8050

= \frac{9 0 ^{2}}{8050}

Factorizar

9 0^{2} : 3^{4} \cdot 2^{2} \cdot 5^{2}

Factorizar

90 = 3^{2} \cdot 2 \cdot 5

= (3^{2} \cdot 2 \cdot 5)^{2}

Aplicar las leyes de los exponentes:

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

= 2^{2} \cdot 5^{2} (3^{2})^{2}

Simplificar

(3^{2})^{2} : 3^{4}

(3^{2})^{2}

Aplicar las leyes de los exponentes:

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

= 3^{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= 3^{4}

= 3^{4} \cdot 2^{2} \cdot 5^{2}

Factorizar

8050 : 5^{2} \cdot 2 \cdot 7 \cdot 23

Factorizar

8050 = 5^{2} \cdot 2 \cdot 7 \cdot 23

= \frac{3 ^{4} \cdot 2 ^{2} \cdot 5 ^{2}}{5 ^{2} \cdot 2 \cdot 7 \cdot 23}

Cancelar

\frac{2 ^{2} \cdot 3 ^{4} \cdot 5 ^{2}}{2 \cdot 5 ^{2} \cdot 7 \cdot 23} : \frac{3 ^{4} \cdot 2}{7 \cdot 23}

\frac{2 ^{2} \cdot 3 ^{4} \cdot 5 ^{2}}{2 \cdot 5 ^{2} \cdot 7 \cdot 23}

Eliminar los terminos comunes:

2

= \frac{3 ^{4} \cdot 5 ^{2} \cdot 2}{5 ^{2} \cdot 7 \cdot 23}

Eliminar los terminos comunes:

5^{2}

= \frac{3 ^{4} \cdot 2}{7 \cdot 23}

= \frac{3 ^{4} \cdot 2}{7 \cdot 23}

Multiplicar los numeros:

7 \cdot 23 = 161

= \frac{3 ^{4} \cdot 2}{161}

3^{4} \cdot 2 = 162

3^{4} \cdot 2

3^{4} = 81

= 81 \cdot 2

Multiplicar los numeros:

81 \cdot 2 = 162

= 162

= \frac{162}{161}

Aplicar propiedades trigonométricas inversas

tan (θ) = \frac{162}{161}

Soluciones generales para

tan (θ) = \frac{162}{161}

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (\frac{162}{161}) + πn

θ = arctan (\frac{162}{161}) + πn

Mostrar soluciones en forma decimal

θ = 0.78849 \dots + πn

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