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Popular >

tan(2θ)=(500)/(350-75)

Solución

tan (2 θ) = \frac{500}{350 - 75}

θ = \frac{1.06795 \dots}{2} + \frac{πn}{2}

radianes

θ = \frac{1.06795 \dots}{2} + \frac{π}{2} n

Pasos de solución

tan (2 θ) = \frac{500}{350 - 75}

Simplificar

\frac{500}{350 - 75} : \frac{20}{11}

\frac{500}{350 - 75}

Restar:

350 - 75 = 275

= \frac{500}{275}

Eliminar los terminos comunes:

25

= \frac{20}{11}

Aplicar propiedades trigonométricas inversas

tan (2 θ) = \frac{20}{11}

Soluciones generales para

tan (2 θ) = \frac{20}{11}

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

2 θ = arctan (\frac{20}{11}) + πn

2 θ = arctan (\frac{20}{11}) + πn

Resolver

2 θ = arctan (\frac{20}{11}) + πn : θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

2 θ = arctan (\frac{20}{11}) + πn

Dividir ambos lados entre

2

2 θ = arctan (\frac{20}{11}) + πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

Simplificar

θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

Mostrar soluciones en forma decimal

θ = \frac{1.06795 \dots}{2} + \frac{πn}{2}

sec (a) = - 2

tan^{2} (γ) + 1 = cos^{2} (γ)

sin^{2} (x) + 8 sin (x) - 9 = 0

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ), 0^{\circ} \leq θ < 36 0^{\circ}

cot^{2} (θ) + 4 csc (θ) = - 5