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Popular >

110^6=(400cos(θ)+700)^2+(400*sin(θ))^2

Solución

1 \cdot 1 0^{6} = (400 \cdot cos (θ) + 700)^{2} + (400 \cdot sin (θ))^{2}

Solución

θ = 0.89566 \dots + 2 πn, θ = 2 π - 0.89566 \dots + 2 πn

+1

Grados

θ = 51.31781 \dots^{\circ} + 36 0^{\circ} n, θ = 308.68218 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

1 \cdot 1 0^{6} = (400 cos (θ) + 700)^{2} + (400 sin (θ))^{2}

Intercambiar lados

(400 cos (θ) + 700)^{2} + (400 sin (θ))^{2} = 1 \cdot 1 0^{6}

Restar

11 0^{6}

de ambos lados

160000 cos^{2} (θ) + 160000 sin^{2} (θ) + 560000 cos (θ) - 510000 = 0

Re-escribir usando identidades trigonométricas

- 510000 + 160000 cos^{2} (θ) + 160000 sin^{2} (θ) + 560000 cos (θ)

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= - 510000 + 160000 (1 - sin^{2} (θ)) + 160000 sin^{2} (θ) + 560000 cos (θ)

Simplificar

- 510000 + 160000 (1 - sin^{2} (θ)) + 160000 sin^{2} (θ) + 560000 cos (θ) : 560000 cos (θ) - 350000

- 510000 + 160000 (1 - sin^{2} (θ)) + 160000 sin^{2} (θ) + 560000 cos (θ)

Expandir

160000 (1 - sin^{2} (θ)) : 160000 - 160000 sin^{2} (θ)

160000 (1 - sin^{2} (θ))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 160000, b = 1, c = sin^{2} (θ)

= 160000 \cdot 1 - 160000 sin^{2} (θ)

Multiplicar los numeros:

160000 \cdot 1 = 160000

= 160000 - 160000 sin^{2} (θ)

= - 510000 + 160000 - 160000 sin^{2} (θ) + 160000 sin^{2} (θ) + 560000 cos (θ)

Simplificar

- 510000 + 160000 - 160000 sin^{2} (θ) + 160000 sin^{2} (θ) + 560000 cos (θ) : 560000 cos (θ) - 350000

- 510000 + 160000 - 160000 sin^{2} (θ) + 160000 sin^{2} (θ) + 560000 cos (θ)

Sumar elementos similares:

- 160000 sin^{2} (θ) + 160000 sin^{2} (θ) = 0

= - 510000 + 160000 + 560000 cos (θ)

Sumar/restar lo siguiente:

- 510000 + 160000 = - 350000

= 560000 cos (θ) - 350000

= 560000 cos (θ) - 350000

= 560000 cos (θ) - 350000

- 350000 + 560000 cos (θ) = 0

Mover

350000

al lado derecho

- 350000 + 560000 cos (θ) = 0

Sumar

350000

a ambos lados

- 350000 + 560000 cos (θ) + 350000 = 0 + 350000

Simplificar

560000 cos (θ) = 350000

560000 cos (θ) = 350000

Dividir ambos lados entre

560000

560000 cos (θ) = 350000

Dividir ambos lados entre

560000

\frac{560000 cos ( θ )}{560000} = \frac{350000}{560000}

Simplificar

cos (θ) = \frac{5}{8}

cos (θ) = \frac{5}{8}

Aplicar propiedades trigonométricas inversas

cos (θ) = \frac{5}{8}

Soluciones generales para

cos (θ) = \frac{5}{8}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{5}{8}) + 2 πn, θ = 2 π - arccos (\frac{5}{8}) + 2 πn

θ = arccos (\frac{5}{8}) + 2 πn, θ = 2 π - arccos (\frac{5}{8}) + 2 πn

Mostrar soluciones en forma decimal

θ = 0.89566 \dots + 2 πn, θ = 2 π - 0.89566 \dots + 2 πn

Ejemplos populares

sin(x)-0.5*cos(x)=0.768

sin (x) - 0.5 \cdot cos (x) = 0.768

((176)^2)/(300*32.2)=tan(θ+30.9637)

\frac{( 176 ) ^{2}}{300 \cdot 32.2} = tan (θ + 30.963 7^{\circ})

sin(x/2)= 1/2 ,0<= ,x<= 360

sin (\frac{x}{2}) = \frac{1}{2}, 0 \leq, x \leq 36 0^{\circ}

- 1 - 2 sin (x) = 0

sin(x)=3cos(x),sin(x)cos(x)

sin (x) = 3 cos (x), sin (x) cos (x)