-3sqrt(3)+7csc(θ/5+23)=5sqrt(3)

Solución

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

Pasos de solución

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

Mover

33

al lado derecho

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

Dividir ambos lados entre

7

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

Aplicar propiedades trigonométricas inversas

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

Resolver

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n : θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

Resolver

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n : θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

Mostrar soluciones en forma decimal

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

10 sin (x) tan (x) + tan (x) = 0

2 sin^{2} (θ) + sin (θ) - 1 = 0, 0 \leq θ \leq 2 π

10 sin (x) cos (x) - 7 cos (x) = 0

sin (x + \frac{π}{4}) - sin (x - \frac{π}{4}) = 1

2 cos^{3} (x) = 2 cos (x)