English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cot(θ))/(csc(θ))=sin(θ)

Solución

\frac{cot ( θ )}{csc ( θ )} = sin (θ)

θ = \frac{π}{4} + πn

Grados

θ = 4 5^{\circ} + 18 0^{\circ} n

Pasos de solución

\frac{cot ( θ )}{csc ( θ )} = sin (θ)

Restar

sin (θ)

de ambos lados

\frac{cot ( θ )}{csc ( θ )} - sin (θ) = 0

Simplificar

\frac{cot ( θ )}{csc ( θ )} - sin (θ) : \frac{cot ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )}

\frac{cot ( θ )}{csc ( θ )} - sin (θ)

Convertir a fracción:

sin (θ) = \frac{sin ( θ ) csc ( θ )}{csc ( θ )}

= \frac{cot ( θ )}{csc ( θ )} - \frac{sin ( θ ) csc ( θ )}{csc ( θ )}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{cot ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )}

\frac{cot ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )} = 0

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

cot (θ) - sin (θ) csc (θ) = 0

Re-escribir usando identidades trigonométricas

cot (θ) - sin (θ) csc (θ)

csc (θ) sin (θ) = 1

csc (θ) sin (θ)

Expresar con seno, coseno

csc (θ) sin (θ)

Utilizar la identidad trigonométrica básica:

csc (θ) = \frac{1}{sin ( θ )}

= \frac{1}{sin ( θ )} sin (θ)

\frac{1}{sin ( θ )} sin (θ) = 1

\frac{1}{sin ( θ )} sin (θ)

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( θ )}{sin ( θ )}

Eliminar los terminos comunes:

sin (θ)

= 1

= 1

= cot (θ) - 1

cot (θ) - 1 = 0

Mover

1

al lado derecho

cot (θ) - 1 = 0

Sumar

1

a ambos lados

cot (θ) - 1 + 1 = 0 + 1

Simplificar

cot (θ) = 1

cot (θ) = 1

Soluciones generales para

cot (θ) = 1

cot (x)

tabla de valores periódicos con

πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

cos (t) = - \frac{2}{3}

sin (θ) = 1 + (1 - (cos (θ) - 1)^{2})

0 = 4 cos (4 x)

tan (θ) = \frac{8}{7}, π < θ < \frac{3 π}{2}

csc (θ) sin (θ) = cot (θ)