English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8cos(x)=3csc(x)

Solución

8 cos (x) = 3 csc (x)

Solución

x = \frac{0.84806 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.84806 \dots}{2} + πn

Grados

x = 24.29518 \dots^{\circ} + 18 0^{\circ} n, x = 65.70481 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

8 cos (x) = 3 csc (x)

Restar

3 csc (x)

de ambos lados

8 cos (x) - 3 csc (x) = 0

Expresar con seno, coseno

- 3 csc (x) + 8 cos (x)

Utilizar la identidad trigonométrica básica:

csc (x) = \frac{1}{sin ( x )}

= - 3 \cdot \frac{1}{sin ( x )} + 8 cos (x)

Simplificar

- 3 \cdot \frac{1}{sin ( x )} + 8 cos (x) : \frac{- 3 + 8 cos ( x ) sin ( x )}{sin ( x )}

- 3 \cdot \frac{1}{sin ( x )} + 8 cos (x)

3 \cdot \frac{1}{sin ( x )} = \frac{3}{sin ( x )}

3 \cdot \frac{1}{sin ( x )}

Multiplicar fracciones:

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

= \frac{1 \cdot 3}{sin ( x )}

Multiplicar los numeros:

1 \cdot 3 = 3

= \frac{3}{sin ( x )}

= - \frac{3}{sin ( x )} + 8 cos (x)

Convertir a fracción:

8 cos (x) = \frac{8 cos ( x ) sin ( x )}{sin ( x )}

= - \frac{3}{sin ( x )} + \frac{8 cos ( x ) sin ( x )}{sin ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- 3 + 8 cos ( x ) sin ( x )}{sin ( x )}

= \frac{- 3 + 8 cos ( x ) sin ( x )}{sin ( x )}

\frac{- 3 + 8 cos ( x ) sin ( x )}{sin ( x )} = 0

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

- 3 + 8 cos (x) sin (x) = 0

Re-escribir usando identidades trigonométricas

- 3 + 8 cos (x) sin (x)

Utilizar la identidad trigonométrica del ángulo doble:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= - 3 + 8 \cdot \frac{sin ( 2 x )}{2}

- 3 + 8 \cdot \frac{sin ( 2 x )}{2} = 0

8 \cdot \frac{sin ( 2 x )}{2} = 4 sin (2 x)

8 \cdot \frac{sin ( 2 x )}{2}

Multiplicar fracciones:

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

= \frac{sin ( 2 x ) \cdot 8}{2}

Dividir:

\frac{8}{2} = 4

= 4 sin (2 x)

- 3 + 4 sin (2 x) = 0

Mover

3

al lado derecho

- 3 + 4 sin (2 x) = 0

Sumar

3

a ambos lados

- 3 + 4 sin (2 x) + 3 = 0 + 3

Simplificar

4 sin (2 x) = 3

4 sin (2 x) = 3

Dividir ambos lados entre

4

4 sin (2 x) = 3

Dividir ambos lados entre

4

\frac{4 sin ( 2 x )}{4} = \frac{3}{4}

Simplificar

sin (2 x) = \frac{3}{4}

sin (2 x) = \frac{3}{4}

Aplicar propiedades trigonométricas inversas

sin (2 x) = \frac{3}{4}

Soluciones generales para

sin (2 x) = \frac{3}{4}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x = arcsin (\frac{3}{4}) + 2 πn, 2 x = π - arcsin (\frac{3}{4}) + 2 πn

2 x = arcsin (\frac{3}{4}) + 2 πn, 2 x = π - arcsin (\frac{3}{4}) + 2 πn

Resolver

2 x = arcsin (\frac{3}{4}) + 2 πn : x = \frac{arcsin ( \frac{3}{4} )}{2} + πn

2 x = arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

2 x = arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arcsin ( \frac{3}{4} )}{2} + πn

x = \frac{arcsin ( \frac{3}{4} )}{2} + πn

Resolver

2 x = π - arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + πn

2 x = π - arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

2 x = π - arcsin (\frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + πn

x = \frac{arcsin ( \frac{3}{4} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + πn

Mostrar soluciones en forma decimal

x = \frac{0.84806 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.84806 \dots}{2} + πn

Ejemplos populares

2sin(x)cos(x)-2sin(x)+cos(x)=1

2 sin (x) cos (x) - 2 sin (x) + cos (x) = 1

8cos(4x)=0

8 cos (4 x) = 0

cos(3x)+sin(5x)=0

cos (3 x) + sin (5 x) = 0

sin^2(o)+3sin(o)-4=0

sin^{2} (o) + 3 sin (o) - 4 = 0

tan(θ)=3.8

tan (θ) = 3.8