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Popular >

sin(x+30)=2cos(x)

Solución

sin (x + 3 0^{\circ}) = 2 cos (x)

Solución

x = 6 0^{\circ} + 18 0^{\circ} n

radianes

x = \frac{π}{3} + πn

Pasos de solución

sin (x + 3 0^{\circ}) = 2 cos (x)

Re-escribir usando identidades trigonométricas

sin (x + 3 0^{\circ}) = 2 cos (x)

Re-escribir usando identidades trigonométricas

sin (x + 3 0^{\circ})

Utilizar la identidad de suma de ángulos:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (x) cos (3 0^{\circ}) + cos (x) sin (3 0^{\circ})

Simplificar

sin (x) cos (3 0^{\circ}) + cos (x) sin (3 0^{\circ}) : \frac{3}{2} sin (x) + \frac{1}{2} cos (x)

sin (x) cos (3 0^{\circ}) + cos (x) sin (3 0^{\circ})

Simplificar

cos (3 0^{\circ}) : \frac{3}{2}

cos (3 0^{\circ})

Utilizar la siguiente identidad trivial:

cos (3 0^{\circ}) = \frac{3}{2}

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2} sin (x) + sin (3 0^{\circ}) cos (x)

Simplificar

sin (3 0^{\circ}) : \frac{1}{2}

sin (3 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (3 0^{\circ}) = \frac{1}{2}

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{3}{2} sin (x) + \frac{1}{2} cos (x)

= \frac{3}{2} sin (x) + \frac{1}{2} cos (x)

\frac{3}{2} sin (x) + \frac{1}{2} cos (x) = 2 cos (x)

\frac{3}{2} sin (x) + \frac{1}{2} cos (x) = 2 cos (x)

Restar

2 cos (x)

de ambos lados

\frac{3}{2} sin (x) - \frac{3}{2} cos (x) = 0

Simplificar

\frac{3}{2} sin (x) - \frac{3}{2} cos (x) : \frac{3 sin ( x ) - 3 cos ( x )}{2}

\frac{3}{2} sin (x) - \frac{3}{2} cos (x)

Multiplicar

\frac{3}{2} sin (x) : \frac{3 sin ( x )}{2}

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

Multiplicar fracciones:

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

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

= \frac{3 sin ( x )}{2} - \frac{3}{2} cos (x)

Multiplicar

\frac{3}{2} cos (x) : \frac{3 cos ( x )}{2}

\frac{3}{2} cos (x)

Multiplicar fracciones:

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

= \frac{3 cos ( x )}{2}

= \frac{3 sin ( x )}{2} - \frac{3 cos ( x )}{2}

Aplicar la regla

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

= \frac{3 sin ( x ) - 3 cos ( x )}{2}

\frac{3 sin ( x ) - 3 cos ( x )}{2} = 0

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

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

cos (x), cos (x) \neq = 0

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

3 tan (x) - 3 = 0

3 tan (x) - 3 = 0

Mover

3

al lado derecho

3 tan (x) - 3 = 0

Sumar

3

a ambos lados

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

Simplificar

3 tan (x) = 3

3 tan (x) = 3

Dividir ambos lados entre

3

3 tan (x) = 3

Dividir ambos lados entre

3

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

Simplificar

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

Simplificar

\frac{3 tan ( x )}{3} : tan (x)

\frac{3 tan ( x )}{3}

Eliminar los terminos comunes:

3

= tan (x)

Simplificar

\frac{3}{3} : 3

\frac{3}{3}

Aplicar las leyes de los exponentes:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

Restar:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

Aplicar las leyes de los exponentes:

3^{\frac{1}{2}} = 3

= 3

tan (x) = 3

tan (x) = 3

tan (x) = 3

Soluciones generales para

tan (x) = 3

tan (x)

tabla de valores periódicos con

18 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 6 0^{\circ} + 18 0^{\circ} n

x = 6 0^{\circ} + 18 0^{\circ} n

Ejemplos populares

(3cos(x)+2sin(x))^2+5sin^2(x)=9-3sqrt(3)

(3 cos (x) + 2 sin (x))^{2} + 5 sin^{2} (x) = 9 - 33

7cos(2x)=7sin^2(x)+5

7 cos (2 x) = 7 sin^{2} (x) + 5

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

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

(cos(x)*cot(x))/(1-sin(x))=3

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

(sin(8))/(30)=(sin(θ))/(120)

\frac{sin ( 8 )}{30} = \frac{sin ( θ )}{120}