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3sin^2(c)-7sin(x)+2=0

Solución

3 sin^{2} (c) - 7 sin (x) + 2 = 0

Solución

x = arcsin (- \frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn, x = π + arcsin (\frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn

Pasos de solución

3 sin^{2} (c) - 7 sin (x) + 2 = 0

Mover

3 sin^{2} (c)

al lado derecho

3 sin^{2} (c) - 7 sin (x) + 2 = 0

Restar

3 sin^{2} (c)

de ambos lados

3 sin^{2} (c) - 7 sin (x) + 2 - 3 sin^{2} (c) = 0 - 3 sin^{2} (c)

Simplificar

- 7 sin (x) + 2 = - 3 sin^{2} (c)

- 7 sin (x) + 2 = - 3 sin^{2} (c)

Mover

2

al lado derecho

- 7 sin (x) + 2 = - 3 sin^{2} (c)

Restar

2

de ambos lados

- 7 sin (x) + 2 - 2 = - 3 sin^{2} (c) - 2

Simplificar

- 7 sin (x) = - 3 sin^{2} (c) - 2

- 7 sin (x) = - 3 sin^{2} (c) - 2

Dividir ambos lados entre

- 7

- 7 sin (x) = - 3 sin^{2} (c) - 2

Dividir ambos lados entre

- 7

\frac{- 7 sin ( x )}{- 7} = - \frac{3 sin ^{2} ( c )}{- 7} - \frac{2}{- 7}

Simplificar

\frac{- 7 sin ( x )}{- 7} = - \frac{3 sin ^{2} ( c )}{- 7} - \frac{2}{- 7}

Simplificar

\frac{- 7 sin ( x )}{- 7} : sin (x)

\frac{- 7 sin ( x )}{- 7}

Aplicar las propiedades de las fracciones:

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

= \frac{7 sin ( x )}{7}

Dividir:

\frac{7}{7} = 1

= sin (x)

Simplificar

- \frac{3 sin ^{2} ( c )}{- 7} - \frac{2}{- 7} : - \frac{- 3 sin ^{2} ( c ) - 2}{7}

- \frac{3 sin ^{2} ( c )}{- 7} - \frac{2}{- 7}

Aplicar la regla

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

= \frac{- 3 sin ^{2} ( c ) - 2}{- 7}

Aplicar las propiedades de las fracciones:

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

= - \frac{- 3 sin ^{2} ( c ) - 2}{7}

sin (x) = - \frac{- 3 sin ^{2} ( c ) - 2}{7}

sin (x) = - \frac{- 3 sin ^{2} ( c ) - 2}{7}

sin (x) = - \frac{- 3 sin ^{2} ( c ) - 2}{7}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{- 3 sin ^{2} ( c ) - 2}{7}

Soluciones generales para

sin (x) = - \frac{- 3 sin ^{2} ( c ) - 2}{7}

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

x = arcsin (- \frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn, x = π + arcsin (\frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn

x = arcsin (- \frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn, x = π + arcsin (\frac{- 3 sin ^{2} ( c ) - 2}{7}) + 2 πn

Ejemplos populares

1+cos^2(x)=sin^4(x)

1 + cos^{2} (x) = sin^{4} (x)

cos (t) = cos (2 t)

arctan(x+2)=arcsin(7/25)+arccos(4/5)

arctan (x + 2) = arcsin (\frac{7}{25}) + arccos (\frac{4}{5})

sec (a) = \frac{38}{13}

tan (c) = 0.6538