Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
pi*a^2/(6*(1-cos(l)))*tan(f)*sqrt((a^2+a*cos(l))/(4/1-cos(l)))
¿Cómo vas a descomponer esta pi*a^2/(6*(1-cos(l)))*tan(f)*sqrt((a^2+a*cos(l))/(4/1-cos(l))) expresión en fracciones?
Solución
Ha introducido
[src]
_______________
2 / 2
pi*a / a + a*cos(l)
--------------*tan(f)* / -------------
6*(1 - cos(l)) \/ 4 - cos(l)
$$\frac{\pi a^{2}}{6 \left(1 - \cos{\left(l \right)}\right)} \tan{\left(f \right)} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}}$$
(((pi*a^2)/((6*(1 - cos(l)))))*tan(f))*sqrt((a^2 + a*cos(l))/(4 - cos(l)))
Simplificación general
[src]
__________________
2 / -a*(a + cos(l))
-pi*a * / ---------------- *tan(f)
\/ -4 + cos(l)
-------------------------------------
-6 + 6*cos(l)
$$- \frac{\pi a^{2} \sqrt{- \frac{a \left(a + \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}$$
-pi*a^2*sqrt(-a*(a + cos(l))/(-4 + cos(l)))*tan(f)/(-6 + 6*cos(l))
Respuesta numérica
[src]
3.14159265358979*a^2*((a^2 + a*cos(l))/(4.0 - cos(l)))^0.5*tan(f)/(6.0 - 6.0*cos(l))
3.14159265358979*a^2*((a^2 + a*cos(l))/(4.0 - cos(l)))^0.5*tan(f)/(6.0 - 6.0*cos(l))
Combinatoria
[src]
________________
2 / a*(a + cos(l))
-pi*a * / -------------- *tan(f)
\/ 4 - cos(l)
-----------------------------------
6*(-1 + cos(l))
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}$$
-pi*a^2*sqrt(a*(a + cos(l))/(4 - cos(l)))*tan(f)/(6*(-1 + cos(l)))
Unión de expresiones racionales
[src]
________________
2 / a*(a + cos(l))
pi*a * / -------------- *tan(f)
\/ 4 - cos(l)
---------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
pi*a^2*sqrt(a*(a + cos(l))/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))
Potencias
[src]
_______________
/ 2
2 / a + a*cos(l)
pi*a * / ------------- *tan(f)
\/ 4 - cos(l)
---------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
_______________________
/ / I*l -I*l\
/ 2 |e e |
/ a + a*|---- + -----|
2 / \ 2 2 / / I*f -I*f\
pi*I*a * / --------------------- *\- e + e /
/ I*l -I*l
/ e e
/ 4 - ---- - -----
\/ 2 2
----------------------------------------------------------
/ I*f -I*f\ / I*l -I*l\
\e + e /*\6 - 3*e - 3*e /
$$\frac{i \pi a^{2} \sqrt{\frac{a^{2} + a \left(\frac{e^{i l}}{2} + \frac{e^{- i l}}{2}\right)}{- \frac{e^{i l}}{2} + 4 - \frac{e^{- i l}}{2}}} \left(- e^{i f} + e^{- i f}\right)}{\left(e^{i f} + e^{- i f}\right) \left(- 3 e^{i l} + 6 - 3 e^{- i l}\right)}$$
pi*i*a^2*sqrt((a^2 + a*(exp(i*l)/2 + exp(-i*l)/2))/(4 - exp(i*l)/2 - exp(-i*l)/2))*(-exp(i*f) + exp(-i*f))/((exp(i*f) + exp(-i*f))*(6 - 3*exp(i*l) - 3*exp(-i*l)))
Denominador racional
[src]
_______________
/ 2
2 / a + a*cos(l)
pi*a * / ------------- *tan(f)
\/ 4 - cos(l)
---------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
pi*a^2*sqrt((a^2 + a*cos(l))/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))
Denominador común
[src]
_________________________
/ 2
2 / a a*cos(l)
-pi*a * / ---------- + ---------- *tan(f)
\/ 4 - cos(l) 4 - cos(l)
---------------------------------------------
-6 + 6*cos(l)
$$- \frac{\pi a^{2} \sqrt{\frac{a^{2}}{4 - \cos{\left(l \right)}} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}$$
-pi*a^2*sqrt(a^2/(4 - cos(l)) + a*cos(l)/(4 - cos(l)))*tan(f)/(-6 + 6*cos(l))
Compilar la expresión
[src]
_______________
/ 2
2 / a + a*cos(l)
pi*a * / ------------- *tan(f)
\/ 4 - cos(l)
---------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
pi*a^2*sqrt((a^2 + a*cos(l))/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))
Parte trigonométrica
[src]
______________________
/ / 2/l\\
/ | -1 + cot |-||
/ | \2/|
/ a*|a + ------------|
/ | 2/l\ |
/ | 1 + cot |-| |
2 / \ \2/ /
-pi*a * / --------------------
/ 2/l\
/ -1 + cot |-|
/ \2/
/ 4 - ------------
/ 2/l\
/ 1 + cot |-|
\/ \2/
----------------------------------------------
/ 2/l\\
| -1 + cot |-||
| \2/|
6*|-1 + ------------|*cot(f)
| 2/l\ |
| 1 + cot |-| |
\ \2/ /
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4}}}{6 \left(\frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} - 1\right) \cot{\left(f \right)}}$$
_______________
/ 2
2 / a + a*cos(l) / pi\
pi*a * / ------------- *cos|f - --|
\/ 4 - cos(l) \ 2 /
--------------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
________________
2 / a*(a + cos(l))
pi*a * / -------------- *tan(f)
\/ 4 - cos(l)
---------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
_______________________
/ / 2/l\\
/ a*|-1 + cot |-||
/ 2 \ \2//
/ a + ----------------
/ 2/l\
/ 1 + cot |-|
2 / \2/
pi*a * / ---------------------
/ 2/l\
/ -1 + cot |-|
/ \2/
/ 4 - ------------
/ 2/l\
/ 1 + cot |-|
\/ \2/
---------------------------------------------
/ / 2/l\\\
| 6*|-1 + cot |-|||
| \ \2//|
|6 - ----------------|*cot(f)
| 2/l\ |
| 1 + cot |-| |
\ \2/ /
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1}}{- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4}}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \cot{\left(f \right)}}$$
__________________
/ 2 a
/ a + -----------
/ /pi \
/ csc|-- - l|
2 / \2 / /pi \
pi*a * / ---------------- *csc|-- - f|
/ 1 \2 /
/ 4 - -----------
/ /pi \
/ csc|-- - l|
\/ \2 /
------------------------------------------------
/ 6 \
|6 - -----------|*csc(f)
| /pi \|
| csc|-- - l||
\ \2 //
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + \frac{a}{\csc{\left(- l + \frac{\pi}{2} \right)}}}{4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{\left(6 - \frac{6}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}$$
_______________
/ 2
2 / a + a*cos(l) 2
2*pi*a * / ------------- *sin (f)
\/ 4 - cos(l)
------------------------------------
(6 - 6*cos(l))*sin(2*f)
$$\frac{2 \pi a^{2} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \sin{\left(2 f \right)}}$$
_____________________
/ / 2/l\\
/ | 1 - tan |-||
/ | \2/|
/ a*|a + -----------|
/ | 2/l\|
/ | 1 + tan |-||
2 / \ \2//
-pi*a * / ------------------- *tan(f)
/ 2/l\
/ 1 - tan |-|
/ \2/
/ 4 - -----------
/ 2/l\
/ 1 + tan |-|
\/ \2/
----------------------------------------------------
/ 2/l\\
| 1 - tan |-||
| \2/|
6*|-1 + -----------|
| 2/l\|
| 1 + tan |-||
\ \2//
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4}} \tan{\left(f \right)}}{6 \left(\frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} - 1\right)}$$
_____________________
/ / 2/l\\
/ | 1 - tan |-||
/ | \2/|
/ a*|a + -----------|
/ | 2/l\|
/ | 1 + tan |-||
2 / \ \2//
pi*a * / ------------------- *tan(f)
/ 2/l\
/ 1 - tan |-|
/ \2/
/ 4 - -----------
/ 2/l\
/ 1 + tan |-|
\/ \2/
--------------------------------------------------
/ 2/l\\
6*|1 - tan |-||
\ \2//
6 - ---------------
2/l\
1 + tan |-|
\2/
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4}} \tan{\left(f \right)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}$$
________________
2 / a*(a + cos(l))
-pi*a * / -------------- *tan(f)
\/ 4 - cos(l)
-----------------------------------
6*(-1 + cos(l))
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}$$
_______________
/ 2
2 / a + a*cos(l)
pi*a * / ------------- *sin(f)
\/ 4 - cos(l)
---------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
_____________________
/ / 1 \
/ a*|a + -----------|
/ | /pi \|
/ | csc|-- - l||
2 / \ \2 // /pi \
-pi*a * / ------------------- *csc|-- - f|
/ 1 \2 /
/ 4 - -----------
/ /pi \
/ csc|-- - l|
\/ \2 /
-----------------------------------------------------
/ 1 \
6*|-1 + -----------|*csc(f)
| /pi \|
| csc|-- - l||
\ \2 //
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right)}{4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{6 \left(-1 + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}$$
________________
/ / 1 \
/ a*|a + ------|
2 / \ sec(l)/
pi*a * / -------------- *sec(f)
/ 1
/ 4 - ------
\/ sec(l)
-------------------------------------
/ 6 \ / pi\
|6 - ------|*sec|f - --|
\ sec(l)/ \ 2 /
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1}{\sec{\left(l \right)}}\right)}{4 - \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}$$
________________
2 / a*(a + cos(l)) / pi\
-pi*a * / -------------- *cos|f - --|
\/ 4 - cos(l) \ 2 /
----------------------------------------
6*(-1 + cos(l))*cos(f)
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{6 \left(\cos{\left(l \right)} - 1\right) \cos{\left(f \right)}}$$
______________________
/ / 2/l\\
/ | -1 + cot |-||
/ | \2/|
/ a*|a + ------------|
/ | 2/l\ |
/ | 1 + cot |-| |
2 / \ \2/ /
pi*a * / --------------------
/ 2/l\
/ -1 + cot |-|
/ \2/
/ 4 - ------------
/ 2/l\
/ 1 + cot |-|
\/ \2/
--------------------------------------------
/ / 2/l\\\
| 6*|-1 + cot |-|||
| \ \2//|
|6 - ----------------|*cot(f)
| 2/l\ |
| 1 + cot |-| |
\ \2/ /
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4}}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \cot{\left(f \right)}}$$
______________________
/ / 2/l\\
/ a*|1 - tan |-||
/ 2 \ \2//
/ a + ---------------
/ 2/l\
/ 1 + tan |-|
2 / \2/
pi*a * / -------------------- *tan(f)
/ 2/l\
/ 1 - tan |-|
/ \2/
/ 4 - -----------
/ 2/l\
/ 1 + tan |-|
\/ \2/
---------------------------------------------------
/ 2/l\\
6*|1 - tan |-||
\ \2//
6 - ---------------
2/l\
1 + tan |-|
\2/
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1}}{- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4}} \tan{\left(f \right)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}$$
_____________________
/ / / pi\\
/ a*|a + sin|l + --||
2 / \ \ 2 // 2
2*pi*a * / ------------------- *sin (f)
/ / pi\
/ 4 - sin|l + --|
\/ \ 2 /
---------------------------------------------
/ / pi\\
|6 - 6*sin|l + --||*sin(2*f)
\ \ 2 //
$$\frac{2 \pi a^{2} \sqrt{\frac{a \left(a + \sin{\left(l + \frac{\pi}{2} \right)}\right)}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(2 f \right)}}$$
_____________
/ 2 a
/ a + ------
2 / sec(l)
pi*a * / ----------- *sec(f)
/ 1
/ 4 - ------
\/ sec(l)
----------------------------------
/ 6 \
|6 - ------|*csc(f)
\ sec(l)/
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + \frac{a}{\sec{\left(l \right)}}}{4 - \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \csc{\left(f \right)}}$$
____________________
/ 2 / pi\
/ a + a*sin|l + --|
2 / \ 2 / 2
2*pi*a * / ------------------ *sin (f)
/ / pi\
/ 4 - sin|l + --|
\/ \ 2 /
--------------------------------------------
/ / pi\\
|6 - 6*sin|l + --||*sin(2*f)
\ \ 2 //
$$\frac{2 \pi a^{2} \sqrt{\frac{a^{2} + a \sin{\left(l + \frac{\pi}{2} \right)}}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(2 f \right)}}$$
________________
2 / a*(a + cos(l)) / pi\
pi*a * / -------------- *cos|f - --|
\/ 4 - cos(l) \ 2 /
--------------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
_____________________
/ / / pi\\
/ a*|a + sin|l + --||
2 / \ \ 2 // 2
-pi*a * / ------------------- *sin (f)
/ / pi\
/ 4 - sin|l + --|
\/ \ 2 /
---------------------------------------------
/ / pi\\
3*|-1 + sin|l + --||*sin(2*f)
\ \ 2 //
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \sin{\left(l + \frac{\pi}{2} \right)}\right)}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{3 \left(\sin{\left(l + \frac{\pi}{2} \right)} - 1\right) \sin{\left(2 f \right)}}$$
_____________________
/ / 1 \
/ a*|a + -----------|
/ | /pi \|
/ | csc|-- - l||
2 / \ \2 // /pi \
pi*a * / ------------------- *csc|-- - f|
/ 1 \2 /
/ 4 - -----------
/ /pi \
/ csc|-- - l|
\/ \2 /
---------------------------------------------------
/ 6 \
|6 - -----------|*csc(f)
| /pi \|
| csc|-- - l||
\ \2 //
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right)}{4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{\left(6 - \frac{6}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}$$
_____________
/ 2 a
/ a + ------
2 / sec(l)
pi*a * / ----------- *sec(f)
/ 1
/ 4 - ------
\/ sec(l)
----------------------------------
/ 6 \ / pi\
|6 - ------|*sec|f - --|
\ sec(l)/ \ 2 /
$$\frac{\pi a^{2} \sqrt{\frac{a^{2} + \frac{a}{\sec{\left(l \right)}}}{4 - \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}$$
________________
/ / 1 \
/ a*|a + ------|
2 / \ sec(l)/
-pi*a * / -------------- *sec(f)
/ 1
/ 4 - ------
\/ sec(l)
---------------------------------------
/ 1 \ / pi\
6*|-1 + ------|*sec|f - --|
\ sec(l)/ \ 2 /
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1}{\sec{\left(l \right)}}\right)}{4 - \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{6 \left(-1 + \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}$$
-pi*a^2*sqrt(a*(a + 1/sec(l))/(4 - 1/sec(l)))*sec(f)/(6*(-1 + 1/sec(l))*sec(f - pi/2))