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1715/70 =tan(45+θ/2)

Solución

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

Solución

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

radianes

θ = 2 \cdot 1.53000 \dots - \frac{π}{2} + 2 πn

Pasos de solución

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

Intercambiar lados

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{1715}{70}

Eliminar los terminos comunes:

35

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Aplicar propiedades trigonométricas inversas

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Soluciones generales para

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

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

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Resolver

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n : θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Mover

4 5^{\circ}

al lado derecho

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Restar

4 5^{\circ}

de ambos lados

4 5^{\circ} + \frac{θ}{2} - 4 5^{\circ} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos lados por

2

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos lados por

2

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiplicar fracciones:

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

= 9 0^{\circ}

Eliminar los terminos comunes:

2

= 9 0^{\circ}

= 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

Mostrar soluciones en forma decimal

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

Ejemplos populares

sin(θ)=-(sqrt(3))/2 ,pi<θ<(3pi)/2

sin (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}

cos(3x)=sin(x-30)

cos (3 x) = sin (x - 3 0^{\circ})

4sin(θ)=4cos(2θ)

4 sin (θ) = 4 cos (2 θ)

tan (5 θ + 30) = 1

885cos(θ)-70=cos(250)

885 cos (θ) - 70 = cos (25 0^{\circ})