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tan(3x+25)*160-1=0

Solución

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

Solución

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{0.34387 \dots}{3}

radianes

x = - \frac{5 π}{108} + \frac{0.34387 \dots}{3} + \frac{π}{3} n

Pasos de solución

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

Mover

1

al lado derecho

tan (3 x + 2 5^{\circ}) 16 0^{\circ} - 1 = 0

Sumar

1

a ambos lados

tan (3 x + 2 5^{\circ}) 16 0^{\circ} - 1 + 1 = 0 + 1

Simplificar

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

Multiplicar ambos lados por

9

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

Multiplicar ambos lados por

9

9 tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1 \cdot 9

Simplificar

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

Dividir ambos lados entre

144 0^{\circ}

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

Dividir ambos lados entre

144 0^{\circ}

\frac{144 0 ^{\circ} tan ( 3 x + 2 5 ^{\circ} )}{144 0 ^{\circ}} = \frac{9}{144 0 ^{\circ}}

Simplificar

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

Aplicar propiedades trigonométricas inversas

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

Soluciones generales para

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

Resolver

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

Mover

2 5^{\circ}

al lado derecho

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

Restar

2 5^{\circ}

de ambos lados

3 x + 2 5^{\circ} - 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

Simplificar

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

Dividir ambos lados entre

3

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

Dividir ambos lados entre

3

\frac{3 x}{3} = \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

Simplificar

\frac{3 x}{3} = \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3} : \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

\frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

Agrupar términos semejantes

= \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

\frac{2 5 ^{\circ}}{3} = 8.33333 \dots^{\circ}

\frac{2 5 ^{\circ}}{3}

Aplicar las propiedades de las fracciones:

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

= \frac{90 0 ^{\circ}}{36 \cdot 3}

Multiplicar los numeros:

36 \cdot 3 = 108

= 8.33333 \dots^{\circ}

= \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

Mostrar soluciones en forma decimal

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{0.34387 \dots}{3}

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