English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

solvefor x,z=sqrt(y)sin(4x)

Solução

resolver para

x, z = y sin (4 x)

Solução

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

Passos da solução

z = y sin (4 x)

Trocar lados

y sin (4 x) = z

Dividir ambos os lados por

y; y \neq = 0

y sin (4 x) = z

Dividir ambos os lados por

y; y \neq = 0

\frac{y sin ( 4 x )}{y} = \frac{z}{y}; y \neq = 0

Simplificar

\frac{y sin ( 4 x )}{y} = \frac{z}{y}

Simplificar

\frac{y sin ( 4 x )}{y} : sin (4 x)

\frac{y sin ( 4 x )}{y}

Eliminar o fator comum:

y

= sin (4 x)

Simplificar

\frac{z}{y} : \frac{z y}{y}

\frac{z}{y}

Multiplicar pelo conjugado

\frac{y}{y}

= \frac{z y}{y y}

y y = y

y y

Aplicar as propriedades dos radicais:

a a = a

y y = y

= y

= \frac{z y}{y}

sin (4 x) = \frac{z y}{y}; y \neq = 0

sin (4 x) = \frac{z y}{y}; y \neq = 0

sin (4 x) = \frac{z y}{y}; y \neq = 0

Aplique as propriedades trigonométricas inversas

sin (4 x) = \frac{z y}{y}

Soluções gerais para

sin (4 x) = \frac{z y}{y}

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

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

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

Resolver

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

4 x = arcsin (\frac{z y}{y}) + 2 πn

Simplificar

arcsin (\frac{z y}{y}) + 2 πn : arcsin (\frac{z}{y}) + 2 πn

arcsin (\frac{z y}{y}) + 2 πn

\frac{z y}{y} = \frac{z}{y}

\frac{z y}{y}

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

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

= \frac{z y ^{\frac{1}{2}}}{y}

Aplicar as propriedades dos expoentes:

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

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

= \frac{z}{y ^{1 - \frac{1}{2}}}

Subtrair:

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

= \frac{z}{y ^{\frac{1}{2}}}

Aplicar as propriedades dos radicais:

a^{\frac{1}{n}} = n a

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

= \frac{z}{y}

= arcsin (\frac{z}{y}) + 2 πn

4 x = arcsin (\frac{z}{y}) + 2 πn

Dividir ambos os lados por

4

4 x = arcsin (\frac{z}{y}) + 2 πn

Dividir ambos os lados por

4

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

Simplificar

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

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

Resolver

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

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

Simplificar

π + arcsin (- \frac{z y}{y}) + 2 πn : π + arcsin (- \frac{z}{y}) + 2 πn

π + arcsin (- \frac{z y}{y}) + 2 πn

\frac{z y}{y} = \frac{z}{y}

\frac{z y}{y}

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

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

= \frac{z y ^{\frac{1}{2}}}{y}

Aplicar as propriedades dos expoentes:

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

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

= \frac{z}{y ^{1 - \frac{1}{2}}}

Subtrair:

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

= \frac{z}{y ^{\frac{1}{2}}}

Aplicar as propriedades dos radicais:

a^{\frac{1}{n}} = n a

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

= \frac{z}{y}

= π + arcsin (- \frac{z}{y}) + 2 πn

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

Dividir ambos os lados por

4

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

Dividir ambos os lados por

4

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

Simplificar

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

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

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

Gráfico

Exemplos populares

csc(x)cot(x)=0

csc (x) cot (x) = 0

1/(csc^2(a))=1-sin^2(a)

\frac{1}{csc ^{2} ( a )} = 1 - sin^{2} (a)

5cos(3x)=-3

5 cos (3 x) = - 3

2sin^2(θ)=sin(θ),0<= θ<= 2pi

2 sin^{2} (θ) = sin (θ), 0 \leq θ \leq 2 π

cos(2x)=cos(4x)

cos (2 x) = cos (4 x)