Sr Examen

Otras calculadoras

sin(2x/3)=a+1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /2*x\        
sin|---| = a + 1
   \ 3 /        
$$\sin{\left(\frac{2 x}{3} \right)} = a + 1$$
Gráfica
Respuesta rápida [src]
              /2*im(x)\    /2*re(x)\        /2*re(x)\     /2*im(x)\
a1 = -1 + cosh|-------|*sin|-------| + I*cos|-------|*sinh|-------|
              \   3   /    \   3   /        \   3   /     \   3   /
$$a_{1} = \sin{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \cosh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} + i \cos{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \sinh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} - 1$$
a1 = sin(2*re(x)/3)*cosh(2*im(x)/3) + i*cos(2*re(x)/3)*sinh(2*im(x)/3) - 1
Suma y producto de raíces [src]
suma
         /2*im(x)\    /2*re(x)\        /2*re(x)\     /2*im(x)\
-1 + cosh|-------|*sin|-------| + I*cos|-------|*sinh|-------|
         \   3   /    \   3   /        \   3   /     \   3   /
$$\sin{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \cosh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} + i \cos{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \sinh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} - 1$$
=
         /2*im(x)\    /2*re(x)\        /2*re(x)\     /2*im(x)\
-1 + cosh|-------|*sin|-------| + I*cos|-------|*sinh|-------|
         \   3   /    \   3   /        \   3   /     \   3   /
$$\sin{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \cosh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} + i \cos{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \sinh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} - 1$$
producto
         /2*im(x)\    /2*re(x)\        /2*re(x)\     /2*im(x)\
-1 + cosh|-------|*sin|-------| + I*cos|-------|*sinh|-------|
         \   3   /    \   3   /        \   3   /     \   3   /
$$\sin{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \cosh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} + i \cos{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \sinh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} - 1$$
=
         /2*im(x)\    /2*re(x)\        /2*re(x)\     /2*im(x)\
-1 + cosh|-------|*sin|-------| + I*cos|-------|*sinh|-------|
         \   3   /    \   3   /        \   3   /     \   3   /
$$\sin{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \cosh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} + i \cos{\left(\frac{2 \operatorname{re}{\left(x\right)}}{3} \right)} \sinh{\left(\frac{2 \operatorname{im}{\left(x\right)}}{3} \right)} - 1$$
-1 + cosh(2*im(x)/3)*sin(2*re(x)/3) + i*cos(2*re(x)/3)*sinh(2*im(x)/3)