Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(40*pi*t+pi)/(80*pi)+sin(32*pi*t+pi)/(64*pi)
¿Cómo vas a descomponer esta sin(40*pi*t+pi)/(80*pi)+sin(32*pi*t+pi)/(64*pi) expresión en fracciones?
Solución
Ha introducido
[src]
sin(40*pi*t + pi) sin(32*pi*t + pi)
----------------- + -----------------
80*pi 64*pi
$$\frac{\sin{\left(32 \pi t + \pi \right)}}{64 \pi} + \frac{\sin{\left(40 \pi t + \pi \right)}}{80 \pi}$$
sin((40*pi)*t + pi)/((80*pi)) + sin((32*pi)*t + pi)/((64*pi))
Simplificación general
[src]
/sin(32*pi*t) sin(40*pi*t)\
-|------------ + ------------|
\ 64 80 /
-------------------------------
pi
$$- \frac{\frac{\sin{\left(32 \pi t \right)}}{64} + \frac{\sin{\left(40 \pi t \right)}}{80}}{\pi}$$
-(sin(32*pi*t)/64 + sin(40*pi*t)/80)/pi
Respuesta numérica
[src]
0.00397887357729738*sin((40*pi)*t + pi) + 0.00497359197162173*sin((32*pi)*t + pi)
0.00397887357729738*sin((40*pi)*t + pi) + 0.00497359197162173*sin((32*pi)*t + pi)
Denominador racional
[src]
-80*pi*sin(32*pi*t) - 64*pi*sin(40*pi*t)
----------------------------------------
2
5120*pi
$$\frac{- 80 \pi \sin{\left(32 \pi t \right)} - 64 \pi \sin{\left(40 \pi t \right)}}{5120 \pi^{2}}$$
(-80*pi*sin(32*pi*t) - 64*pi*sin(40*pi*t))/(5120*pi^2)
Unión de expresiones racionales
[src]
4*sin(pi*(1 + 40*t)) + 5*sin(pi*(1 + 32*t))
-------------------------------------------
320*pi
$$\frac{5 \sin{\left(\pi \left(32 t + 1\right) \right)} + 4 \sin{\left(\pi \left(40 t + 1\right) \right)}}{320 \pi}$$
(4*sin(pi*(1 + 40*t)) + 5*sin(pi*(1 + 32*t)))/(320*pi)
Denominador común
[src]
-(4*sin(40*pi*t) + 5*sin(32*pi*t))
-----------------------------------
320*pi
$$- \frac{5 \sin{\left(32 \pi t \right)} + 4 \sin{\left(40 \pi t \right)}}{320 \pi}$$
-(4*sin(40*pi*t) + 5*sin(32*pi*t))/(320*pi)
Potencias
[src]
sin(32*pi*t) sin(40*pi*t)
- ------------ - ------------
64*pi 80*pi
$$- \frac{\sin{\left(32 \pi t \right)}}{64 \pi} - \frac{\sin{\left(40 \pi t \right)}}{80 \pi}$$
/ I*(-pi - 32*pi*t) I*(pi + 32*pi*t)\ / I*(-pi - 40*pi*t) I*(pi + 40*pi*t)\
I*\- e + e / I*\- e + e /
- -------------------------------------------- - --------------------------------------------
128*pi 160*pi
$$- \frac{i \left(- e^{i \left(- 40 \pi t - \pi\right)} + e^{i \left(40 \pi t + \pi\right)}\right)}{160 \pi} - \frac{i \left(- e^{i \left(- 32 \pi t - \pi\right)} + e^{i \left(32 \pi t + \pi\right)}\right)}{128 \pi}$$
-i*(-exp(i*(-pi - 32*pi*t)) + exp(i*(pi + 32*pi*t)))/(128*pi) - i*(-exp(i*(-pi - 40*pi*t)) + exp(i*(pi + 40*pi*t)))/(160*pi)
Combinatoria
[src]
-(4*sin(40*pi*t) + 5*sin(32*pi*t))
-----------------------------------
320*pi
$$- \frac{5 \sin{\left(32 \pi t \right)} + 4 \sin{\left(40 \pi t \right)}}{320 \pi}$$
-(4*sin(40*pi*t) + 5*sin(32*pi*t))/(320*pi)