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Popular >

3tan(x)=sin(x)

Solución

3 tan (x) = sin (x)

x = 2 πn, x = π + 2 πn

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

3 tan (x) = sin (x)

Restar

sin (x)

de ambos lados

3 tan (x) - sin (x) = 0

Expresar con seno, coseno

- sin (x) + 3 tan (x)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

Multiplicar

3 \cdot \frac{sin ( x )}{cos ( x )} : \frac{3 sin ( x )}{cos ( x )}

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

Multiplicar fracciones:

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

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

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

Convertir a fracción:

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

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

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

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

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

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

Factorizar

3 sin (x) - cos (x) sin (x) : - sin (x) (cos (x) - 3)

3 sin (x) - cos (x) sin (x)

Factorizar el termino común

- sin (x)

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

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

Resolver cada parte por separado

sin (x) = 0 or cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

Soluciones generales para

sin (x) = 0

tabla de valores periódicos con

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) - 3 = 0 :

Sin solución

cos (x) - 3 = 0

Mover

3

al lado derecho

cos (x) - 3 = 0

Sumar

3

a ambos lados

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

Simplificar

cos (x) = 3

cos (x) = 3

- 1 \leq cos (x) \leq 1

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn

5 = sinh (x)

- 16 cos (2 x) = 0

62 + 12 cos (x - 4 5^{\circ}) = 0

(2 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

\frac{1}{tan ( x )} = 0.5