sin(θ)= 4/5 cos(θ)

Solución

sin (θ) = \frac{4}{5} cos (θ)

θ = 0.67474 \dots + πn

Grados

θ = 38.65980 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

sin (θ) = \frac{4}{5} cos (θ)

Re-escribir usando identidades trigonométricas

sin (θ) = \frac{4}{5} cos (θ)

Dividir ambos lados entre

cos (θ), cos (θ) \neq = 0

\frac{sin ( θ )}{cos ( θ )} = \frac{\frac{4}{5} cos ( θ )}{cos ( θ )}

Simplificar

\frac{sin ( θ )}{cos ( θ )} = \frac{4}{5}

Utilizar la identidad trigonométrica básica:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (θ) = \frac{4}{5}

tan (θ) = \frac{4}{5}

Aplicar propiedades trigonométricas inversas

tan (θ) = \frac{4}{5}

Soluciones generales para

tan (θ) = \frac{4}{5}

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

θ = arctan (\frac{4}{5}) + πn

θ = arctan (\frac{4}{5}) + πn

Mostrar soluciones en forma decimal

θ = 0.67474 \dots + πn

19 = \frac{1}{2} \cdot 7.9 \cdot 6.2 sin (x)

cos (x) = - 0.71

tan (α) = \frac{8}{10}

sin (2 x) + 2 \cdot cos (x) = 0

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}