sin(θ)=(0.3924)/(cos(θ))

Solución

sin (θ) = \frac{0.3924}{cos ( θ )}

θ = \frac{0.90237 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.90237 \dots}{2} + πn

Pasos de solución

sin (θ) = \frac{0.3924}{cos ( θ )}

Restar

\frac{0.3924}{cos ( θ )}

de ambos lados

sin (θ) - \frac{0.3924}{cos ( θ )} = 0

Simplificar

sin (θ) - \frac{0.3924}{cos ( θ )} : \frac{sin ( θ ) cos ( θ ) - 0.3924}{cos ( θ )}

\frac{sin ( θ ) cos ( θ ) - 0.3924}{cos ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

sin (θ) cos (θ) - 0.3924 = 0

Re-escribir usando identidades trigonométricas

- 0.3924 + \frac{sin ( 2 θ )}{2} = 0

Mover

0.3924

al lado derecho

\frac{sin ( 2 θ )}{2} = 0.3924

Multiplicar ambos lados por

2

sin (2 θ) = 0.7848

Aplicar propiedades trigonométricas inversas

2 θ = arcsin (0.7848) + 2 πn, 2 θ = π - arcsin (0.7848) + 2 πn

Resolver

2 θ = arcsin (0.7848) + 2 πn : θ = \frac{arcsin ( 0.7848 )}{2} + πn

Resolver

2 θ = π - arcsin (0.7848) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + πn

θ = \frac{arcsin ( 0.7848 )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + πn

Mostrar soluciones en forma decimal

θ = \frac{0.90237 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.90237 \dots}{2} + πn

x, y = 3 sin (x)

6 - 4 cos^{2} (x) - 5 cos (x) = 0

cos (x) = \frac{32}{34.54}

tan (a) = \frac{51}{140}

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