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sinx-cosx=2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(x) - cos(x) = 2
$$\sin{\left(x \right)} - \cos{\left(x \right)} = 2$$
Gráfica
Respuesta rápida [src]
         /    /        ___\\         /    /        ___\\
x1 = 2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 //
$$x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}$$
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x2 = 2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}$$
x2 = 2*re(atan(1 + sqrt(2)*i)) + 2*i*im(atan(1 + sqrt(2)*i))
Suma y producto de raíces [src]
suma
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2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 // + 2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 //
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
=
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2*re\atan\1 + I*\/ 2 // + 2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}$$
producto
/    /    /        ___\\         /    /        ___\\\ /    /    /        ___\\         /    /        ___\\\
\2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 ///*\2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 ///
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
=
  /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
4*\I*im\atan\1 + I*\/ 2 // + re\atan\1 + I*\/ 2 ///*\I*im\atan\1 - I*\/ 2 // + re\atan\1 - I*\/ 2 ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
4*(i*im(atan(1 + i*sqrt(2))) + re(atan(1 + i*sqrt(2))))*(i*im(atan(1 - i*sqrt(2))) + re(atan(1 - i*sqrt(2))))
Respuesta numérica [src]
x1 = 2.35619449019234 - 0.881373587019543*i
x2 = 2.35619449019234 + 0.881373587019543*i
x2 = 2.35619449019234 + 0.881373587019543*i