English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos(α-30))/1 =(sin(60))/3

Solución

\frac{cos ( α - 3 0 ^{\circ} )}{1} = \frac{sin ( 6 0 ^{\circ} )}{3}

Solución

α = 1.27795 \dots + 36 0^{\circ} n + 3 0^{\circ}, α = 36 0^{\circ} - 1.27795 \dots + 36 0^{\circ} n + 3 0^{\circ}

radianes

α = 1.27795 \dots + \frac{π}{6} + 2 πn, α = 2 π - 1.27795 \dots + \frac{π}{6} + 2 πn

Pasos de solución

\frac{cos ( α - 3 0 ^{\circ} )}{1} = \frac{sin ( 6 0 ^{\circ} )}{3}

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

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{3}{2}

= \frac{3}{2}

\frac{cos ( α - 3 0 ^{\circ} )}{1} = \frac{\frac{3}{2}}{3}

Aplicar la regla

\frac{a}{1} = a

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

Aplicar las propiedades de las fracciones:

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

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

Multiplicar los numeros:

2 \cdot 3 = 6

cos (α - 3 0^{\circ}) = \frac{3}{6}

Aplicar propiedades trigonométricas inversas

cos (α - 3 0^{\circ}) = \frac{3}{6}

Soluciones generales para

cos (α - 3 0^{\circ}) = \frac{3}{6}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

α - 3 0^{\circ} = arccos (\frac{3}{6}) + 36 0^{\circ} n, α - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{6}) + 36 0^{\circ} n

α - 3 0^{\circ} = arccos (\frac{3}{6}) + 36 0^{\circ} n, α - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{6}) + 36 0^{\circ} n

Resolver

α - 3 0^{\circ} = arccos (\frac{3}{6}) + 36 0^{\circ} n : α = arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

α - 3 0^{\circ} = arccos (\frac{3}{6}) + 36 0^{\circ} n

Simplificar

arccos (\frac{3}{6}) + 36 0^{\circ} n : arccos (\frac{1}{2 3}) + 36 0^{\circ} n

arccos (\frac{3}{6}) + 36 0^{\circ} n

\frac{3}{6} = \frac{1}{2 3}

\frac{3}{6}

Factorizar

6 : 2 \cdot 3

Factorizar

6 = 2 \cdot 3

= \frac{3}{2 \cdot 3}

Cancelar

\frac{3}{2 \cdot 3} : \frac{1}{2 3}

\frac{3}{2 \cdot 3}

Aplicar las leyes de los exponentes:

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

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

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Restar:

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

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

Aplicar las leyes de los exponentes:

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

= \frac{1}{2 3}

= \frac{1}{2 3}

= arccos (\frac{1}{2 3}) + 36 0^{\circ} n

α - 3 0^{\circ} = arccos (\frac{1}{2 3}) + 36 0^{\circ} n

Mover

3 0^{\circ}

al lado derecho

α - 3 0^{\circ} = arccos (\frac{1}{2 3}) + 36 0^{\circ} n

Sumar

3 0^{\circ}

a ambos lados

α - 3 0^{\circ} + 3 0^{\circ} = arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

Simplificar

α = arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

α = arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

Resolver

α - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{6}) + 36 0^{\circ} n : α = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

α - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{6}) + 36 0^{\circ} n

Simplificar

36 0^{\circ} - arccos (\frac{3}{6}) + 36 0^{\circ} n : 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n

36 0^{\circ} - arccos (\frac{3}{6}) + 36 0^{\circ} n

\frac{3}{6} = \frac{1}{2 3}

\frac{3}{6}

Factorizar

6 : 2 \cdot 3

Factorizar

6 = 2 \cdot 3

= \frac{3}{2 \cdot 3}

Cancelar

\frac{3}{2 \cdot 3} : \frac{1}{2 3}

\frac{3}{2 \cdot 3}

Aplicar las leyes de los exponentes:

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

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

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Restar:

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

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

Aplicar las leyes de los exponentes:

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

= \frac{1}{2 3}

= \frac{1}{2 3}

= 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n

α - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n

Mover

3 0^{\circ}

al lado derecho

α - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n

Sumar

3 0^{\circ}

a ambos lados

α - 3 0^{\circ} + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

Simplificar

α = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

α = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

α = arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}, α = 36 0^{\circ} - arccos (\frac{1}{2 3}) + 36 0^{\circ} n + 3 0^{\circ}

Mostrar soluciones en forma decimal

α = 1.27795 \dots + 36 0^{\circ} n + 3 0^{\circ}, α = 36 0^{\circ} - 1.27795 \dots + 36 0^{\circ} n + 3 0^{\circ}

Ejemplos populares

tan(x)tan(7x)=1,x

tan (x) tan (7 x) = 1, x

3sec^2(x)+tan(x)-6=0

3 sec^{2} (x) + tan (x) - 6 = 0

2sin(x)+cot(x)=csc(x)

2 sin (x) + cot (x) = csc (x)

8cos^2(x)+2cos(x)-3=0

8 cos^{2} (x) + 2 cos (x) - 3 = 0

cos(A)= 1/(sqrt(65)),cos(B)= 1/(sqrt(5))

cos (A) = \frac{1}{65}, cos (B) = \frac{1}{5}