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 _________________
pi*a / 2 a*cos(l)
--------------*tan(f)* / a + ----------
6*(1 - cos(l)) \/ 4 - cos(l)
$$\frac{\pi a^{2}}{6 \left(1 - \cos{\left(l \right)}\right)} \tan{\left(f \right)} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}}$$
(((pi*a^2)/((6*(1 - cos(l)))))*tan(f))*sqrt(a^2 + (a*cos(l))/(4 - cos(l)))
Simplificación general
[src]
_______________________________
2 / a*(-cos(l) + a*(-4 + cos(l)))
-pi*a * / ----------------------------- *tan(f)
\/ -4 + cos(l)
--------------------------------------------------
-6 + 6*cos(l)
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a \left(\cos{\left(l \right)} - 4\right) - \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}$$
-pi*a^2*sqrt(a*(-cos(l) + a*(-4 + cos(l)))/(-4 + cos(l)))*tan(f)/(-6 + 6*cos(l))
Respuesta numérica
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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))
Denominador racional
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_______________________________
2 / a*(-cos(l) + a*(-4 + cos(l)))
-pi*a * / ----------------------------- *tan(f)
\/ -4 + cos(l)
--------------------------------------------------
-6 + 6*cos(l)
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a \left(\cos{\left(l \right)} - 4\right) - \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}$$
-pi*a^2*sqrt(a*(-cos(l) + a*(-4 + cos(l)))/(-4 + cos(l)))*tan(f)/(-6 + 6*cos(l))
Unión de expresiones racionales
[src]
_____________________________
2 / a*(a*(4 - cos(l)) + cos(l))
pi*a * / --------------------------- *tan(f)
\/ 4 - cos(l)
----------------------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{\frac{a \left(a \left(4 - \cos{\left(l \right)}\right) + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
pi*a^2*sqrt(a*(a*(4 - cos(l)) + cos(l))/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))
Combinatoria
[src]
________________________________
2 / -a*(-cos(l) - 4*a + a*cos(l))
-pi*a * / ------------------------------ *tan(f)
\/ 4 - cos(l)
---------------------------------------------------
6*(-1 + cos(l))
$$- \frac{\pi a^{2} \sqrt{- \frac{a \left(a \cos{\left(l \right)} - 4 a - \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}$$
-pi*a^2*sqrt(-a*(-cos(l) - 4*a + a*cos(l))/(4 - cos(l)))*tan(f)/(6*(-1 + cos(l)))
Denominador común
[src]
_________________
2 / 2 a*cos(l)
-pi*a * / a + ---------- *tan(f)
\/ 4 - cos(l)
------------------------------------
-6 + 6*cos(l)
$$- \frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}$$
-pi*a^2*sqrt(a^2 + a*cos(l)/(4 - cos(l)))*tan(f)/(-6 + 6*cos(l))
Potencias
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_________________
2 / 2 a*cos(l)
pi*a * / a + ---------- *tan(f)
\/ 4 - cos(l)
----------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
_______________________
/ / I*l -I*l\
/ |e e |
/ a*|---- + -----|
2 / 2 \ 2 2 / / I*f -I*f\
pi*I*a * / 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 /
$$\frac{i \pi a^{2} \sqrt{a^{2} + \frac{a \left(\frac{e^{i l}}{2} + \frac{e^{- i l}}{2}\right)}{- \frac{e^{i l}}{2} + 4 - \frac{e^{- i l}}{2}}} \left(- e^{i f} + e^{- i f}\right)}{\left(e^{i f} + e^{- i f}\right) \left(- 3 e^{i l} + 6 - 3 e^{- i l}\right)}$$
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)))
Compilar la expresión
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_________________
2 / 2 a*cos(l)
pi*a * / a + ---------- *tan(f)
\/ 4 - cos(l)
----------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
pi*a^2*sqrt(a^2 + a*cos(l)/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))
Parte trigonométrica
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____________________________________
2 / 2 a /pi \
pi*a * / a + ----------------------------- *csc|-- - f|
/ / 1 \ /pi \ \2 /
/ |4 - -----------|*csc|-- - l|
/ | /pi \| \2 /
/ | csc|-- - l||
\/ \ \2 //
--------------------------------------------------------------
/ 6 \
|6 - -----------|*csc(f)
| /pi \|
| csc|-- - l||
\ \2 //
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a}{\left(4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(- l + \frac{\pi}{2} \right)}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{\left(6 - \frac{6}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}$$
_________________
2 / 2 a*cos(l) / pi\
pi*a * / a + ---------- *cos|f - --|
\/ 4 - cos(l) \ 2 /
---------------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
_____________________________________
/ / 1 a \
/ a*|----------- + 4*a - -----------|
/ | /pi \ /pi \|
/ |csc|-- - l| csc|-- - l||
2 / \ \2 / \2 // /pi \
-pi*a * / ----------------------------------- *csc|-- - f|
/ 1 \2 /
/ 4 - -----------
/ /pi \
/ csc|-- - l|
\/ \2 /
---------------------------------------------------------------------
/ 1 \
6*|-1 + -----------|*csc(f)
| /pi \|
| csc|-- - l||
\ \2 //
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(4 a - \frac{a}{\csc{\left(- l + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right)}{4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{6 \left(-1 + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}$$
______________________
/ / 2 \
/ a*|1 - -------|
/ | 2/l\|
/ | sec |-||
2 / 2 \ \2//
pi*a * / a + --------------- *sec(f)
/ 1
/ -4 + ------
\/ sec(l)
---------------------------------------------
/ 6 \ / pi\
|6 - ------|*sec|f - --|
\ sec(l)/ \ 2 /
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \frac{2}{\sec^{2}{\left(\frac{l}{2} \right)}}\right)}{-4 + \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}$$
_________________
2 / 2 a*cos(l)
pi*a * / a + ---------- *tan(f)
\/ 4 - cos(l)
----------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
__________________
2 / 2 a*cos(l)
pi*a * / a - ----------- *tan(f)
\/ -4 + cos(l)
-----------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} - \frac{a \cos{\left(l \right)}}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
_________________________________________
/ / 2/l\ / 2/l\\\
/ | 1 - tan |-| a*|1 - tan |-|||
/ | \2/ \ \2//|
/ a*|4*a + ----------- - ---------------|
/ | 2/l\ 2/l\ |
/ | 1 + tan |-| 1 + tan |-| |
2 / \ \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//
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(- \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4 a + \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4}} \tan{\left(f \right)}}{6 \left(\frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} - 1\right)}$$
______________________
/ / pi\
/ a*sin|l + --|
2 / 2 \ 2 / 2
2*pi*a * / a + --------------- *sin (f)
/ / pi\
/ 4 - sin|l + --|
\/ \ 2 /
----------------------------------------------
/ / pi\\
|6 - 6*sin|l + --||*sin(2*f)
\ \ 2 //
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \sin{\left(l + \frac{\pi}{2} \right)}}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(2 f \right)}}$$
_______________________________________
/ / 2/l\\
/ a*|-1 + cot |-||
2 / 2 \ \2// /f\
2*pi*a * / a + -------------------------------- *cot|-|
/ / 2/l\\ \2/
/ | -1 + cot |-||
/ / 2/l\\ | \2/|
/ |1 + cot |-||*|4 - ------------|
/ \ \2// | 2/l\ |
/ | 1 + cot |-| |
\/ \ \2/ /
------------------------------------------------------------------
/ / 2/l\\\
| 6*|-1 + cot |-|||
/ 2/f\\ | \ \2//|
|-1 + cot |-||*|6 - ----------------|
\ \2// | 2/l\ |
| 1 + cot |-| |
\ \2/ /
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\left(- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\cot^{2}{\left(\frac{l}{2} \right)} + 1\right)}} \cot{\left(\frac{f}{2} \right)}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \left(\cot^{2}{\left(\frac{f}{2} \right)} - 1\right)}$$
_________________
2 / 2 a*cos(l) 2
2*pi*a * / a + ---------- *sin (f)
\/ 4 - cos(l)
-------------------------------------
(6 - 6*cos(l))*sin(2*f)
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \sin{\left(2 f \right)}}$$
___________________________
/ / 2 \
/ a*|1 - ------------|
/ | 2/pi l\|
/ | csc |-- - -||
2 / 2 \ \2 2// /pi \
pi*a * / a + -------------------- *csc|-- - f|
/ 1 \2 /
/ -4 + -----------
/ /pi \
/ csc|-- - l|
\/ \2 /
---------------------------------------------------------
/ 6 \
|6 - -----------|*csc(f)
| /pi \|
| csc|-- - l||
\ \2 //
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \frac{2}{\csc^{2}{\left(- \frac{l}{2} + \frac{\pi}{2} \right)}}\right)}{-4 + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{\left(6 - \frac{6}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}$$
_____________________________
/ / 2/pi l\\
/ a*|1 - 2*sin |-- + -||
2 / 2 \ \2 2// 2
2*pi*a * / a + ---------------------- *sin (f)
/ / pi\
/ -4 + sin|l + --|
\/ \ 2 /
-----------------------------------------------------
/ / pi\\
|6 - 6*sin|l + --||*sin(2*f)
\ \ 2 //
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \sin^{2}{\left(\frac{l}{2} + \frac{\pi}{2} \right)}\right)}{\sin{\left(l + \frac{\pi}{2} \right)} - 4}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(2 f \right)}}$$
________________________
/ / 2/l\\
/ a*|1 - 2*cos |-||
2 / 2 \ \2//
pi*a * / a + ----------------- *tan(f)
\/ -4 + cos(l)
-------------------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
_______________________________________
/ / / pi\ / pi\\
/ a*|4*a - a*sin|l + --| + sin|l + --||
2 / \ \ 2 / \ 2 // 2
-pi*a * / ------------------------------------- *sin (f)
/ / pi\
/ 4 - sin|l + --|
\/ \ 2 /
---------------------------------------------------------------
/ / pi\\
3*|-1 + sin|l + --||*sin(2*f)
\ \ 2 //
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(- a \sin{\left(l + \frac{\pi}{2} \right)} + 4 a + \sin{\left(l + \frac{\pi}{2} \right)}\right)}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{3 \left(\sin{\left(l + \frac{\pi}{2} \right)} - 1\right) \sin{\left(2 f \right)}}$$
___________________________________________
/ / 2/l\ / 2/l\\\
/ | -1 + cot |-| a*|-1 + cot |-|||
/ | \2/ \ \2//|
/ a*|4*a + ------------ - ----------------|
/ | 2/l\ 2/l\ |
/ | 1 + cot |-| 1 + cot |-| |
2 / \ \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/ /
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(- \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4 a + \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4}}}{6 \left(\frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} - 1\right) \cot{\left(f \right)}}$$
_______________________________________
/ / 2/l\\
/ a*|-1 + cot |-||
2 / 2 \ \2//
pi*a * / a + --------------------------------
/ / 2/l\\
/ | -1 + cot |-||
/ / 2/l\\ | \2/|
/ |1 + cot |-||*|4 - ------------|
/ \ \2// | 2/l\ |
/ | 1 + cot |-| |
\/ \ \2/ /
---------------------------------------------------------
/ / 2/l\\\
| 6*|-1 + cot |-|||
| \ \2//|
|6 - ----------------|*cot(f)
| 2/l\ |
| 1 + cot |-| |
\ \2/ /
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\left(- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\cot^{2}{\left(\frac{l}{2} \right)} + 1\right)}}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \cot{\left(f \right)}}$$
______________________
/ / pi\
/ a*sin|l + --|
2 / 2 \ 2 /
pi*a * / a + --------------- *sin(f)
/ / pi\
/ 4 - sin|l + --|
\/ \ 2 /
-------------------------------------------
/ / pi\\ / pi\
|6 - 6*sin|l + --||*sin|f + --|
\ \ 2 // \ 2 /
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \sin{\left(l + \frac{\pi}{2} \right)}}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(f + \frac{\pi}{2} \right)}}$$
_____________________________
2 / a*(4*a - a*cos(l) + cos(l))
-pi*a * / --------------------------- *tan(f)
\/ 4 - cos(l)
------------------------------------------------
6*(-1 + cos(l))
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(- a \cos{\left(l \right)} + 4 a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}$$
___________________________
/ / 1 a \
/ a*|------ + 4*a - ------|
2 / \sec(l) sec(l)/
-pi*a * / ------------------------- *sec(f)
/ 1
/ 4 - ------
\/ sec(l)
--------------------------------------------------
/ 1 \ / pi\
6*|-1 + ------|*sec|f - --|
\ sec(l)/ \ 2 /
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(4 a - \frac{a}{\sec{\left(l \right)}} + \frac{1}{\sec{\left(l \right)}}\right)}{4 - \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{6 \left(-1 + \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}$$
__________________
2 / 2 a*cos(l)
pi*a * / a - ----------- *sec(f)*sin(f)
\/ -4 + cos(l)
------------------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} - \frac{a \cos{\left(l \right)}}{\cos{\left(l \right)} - 4}} \sin{\left(f \right)} \sec{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
________________________
/ / 2/l\\
/ a*|1 - 2*cos |-||
2 / 2 \ \2// /f\
2*pi*a * / a + ----------------- *tan|-|
\/ -4 + cos(l) \2/
---------------------------------------------
/ 2/f\\
|1 - tan |-||*(6 - 6*cos(l))
\ \2//
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(\frac{f}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{f}{2} \right)}\right) \left(6 - 6 \cos{\left(l \right)}\right)}$$
_________________
2 / 2 a*cos(l)
pi*a * / a + ---------- *sin(f)
\/ 4 - cos(l)
----------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
______________________________
2 / a*(-cos(l) - 4*a + a*cos(l))
-pi*a * / ---------------------------- *tan(f)
\/ -4 + cos(l)
-------------------------------------------------
6*(-1 + cos(l))
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(a \cos{\left(l \right)} - 4 a - \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}$$
_____________________________
2 / a*(4*a - a*cos(l) + cos(l)) / pi\
-pi*a * / --------------------------- *cos|f - --|
\/ 4 - cos(l) \ 2 /
-----------------------------------------------------
6*(-1 + cos(l))*cos(f)
$$- \frac{\pi a^{2} \sqrt{\frac{a \left(- a \cos{\left(l \right)} + 4 a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{6 \left(\cos{\left(l \right)} - 1\right) \cos{\left(f \right)}}$$
________________________
/ / 2/l\\
/ a*|1 - 2*cos |-||
2 / 2 \ \2// / pi\
pi*a * / a + ----------------- *cos|f - --|
\/ -4 + cos(l) \ 2 /
------------------------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \cos{\left(f - \frac{\pi}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
________________________________
/ / 2\
/ | / 2/l\\ |
/ | 2*|-1 + cot |-|| |
/ | \ \4// |
/ a*|1 - -----------------|
/ | 2 |
/ | / 2/l\\ |
/ | |1 + cot |-|| |
2 / 2 \ \ \4// /
pi*a * / 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/ /
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(- \frac{2 \left(\cot^{2}{\left(\frac{l}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{l}{4} \right)} + 1\right)^{2}} + 1\right)}{\frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} - 4}}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \cot{\left(f \right)}}$$
______________________________________
/ / 2/l\\
/ a*|1 - tan |-||
2 / 2 \ \2//
pi*a * / a + ------------------------------- *tan(f)
/ / 2/l\\
/ | 1 - tan |-||
/ / 2/l\\ | \2/|
/ |1 + tan |-||*|4 - -----------|
/ \ \2// | 2/l\|
/ | 1 + tan |-||
\/ \ \2//
---------------------------------------------------------------
/ 2/l\\
6*|1 - tan |-||
\ \2//
6 - ---------------
2/l\
1 + tan |-|
\2/
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\left(- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\tan^{2}{\left(\frac{l}{2} \right)} + 1\right)}} \tan{\left(f \right)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}$$
__________________________
2 / 2 a
pi*a * / a + ------------------- *sec(f)
/ / 1 \
/ |4 - ------|*sec(l)
\/ \ sec(l)/
---------------------------------------------
/ 6 \ / pi\
|6 - ------|*sec|f - --|
\ sec(l)/ \ 2 /
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a}{\left(4 - \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(l \right)}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}$$
_______________________________
/ / 2\
/ | / 2/l\\ |
/ | 2*|1 - tan |-|| |
/ | \ \4// |
/ a*|1 - ----------------|
/ | 2 |
/ | / 2/l\\ |
/ | |1 + tan |-|| |
2 / 2 \ \ \4// /
pi*a * / 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/
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(- \frac{2 \left(1 - \tan^{2}{\left(\frac{l}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{l}{4} \right)} + 1\right)^{2}} + 1\right)}{\frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} - 4}} \tan{\left(f \right)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}$$
__________________________
2 / 2 a
pi*a * / a + ------------------- *sec(f)
/ / 1 \
/ |4 - ------|*sec(l)
\/ \ sec(l)/
---------------------------------------------
/ 6 \
|6 - ------|*csc(f)
\ sec(l)/
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a}{\left(4 - \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(l \right)}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \csc{\left(f \right)}}$$
______________________________________
/ / 2/l\\
/ a*|1 - tan |-||
2 / 2 \ \2// /f\
2*pi*a * / a + ------------------------------- *tan|-|
/ / 2/l\\ \2/
/ | 1 - tan |-||
/ / 2/l\\ | \2/|
/ |1 + tan |-||*|4 - -----------|
/ \ \2// | 2/l\|
/ | 1 + tan |-||
\/ \ \2//
-----------------------------------------------------------------
/ / 2/l\\\
| 6*|1 - tan |-|||
/ 2/f\\ | \ \2//|
|1 - tan |-||*|6 - ---------------|
\ \2// | 2/l\ |
| 1 + tan |-| |
\ \2/ /
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\left(- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\tan^{2}{\left(\frac{l}{2} \right)} + 1\right)}} \tan{\left(\frac{f}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{f}{2} \right)}\right) \left(- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right)}$$
_________________
2 / 2 a*cos(l)
pi*a * / a + ---------- *sec(f)*sin(f)
\/ 4 - cos(l)
-----------------------------------------
6 - 6*cos(l)
$$\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin{\left(f \right)} \sec{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}$$
________________________
/ / 2/l\\
/ a*|1 - 2*cos |-||
2 / 2 \ \2// /f\
2*pi*a * / a + ----------------- *cot|-|
\/ -4 + cos(l) \2/
---------------------------------------------
/ 2/f\\
|-1 + cot |-||*(6 - 6*cos(l))
\ \2//
$$\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \cot{\left(\frac{f}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \left(\cot^{2}{\left(\frac{f}{2} \right)} - 1\right)}$$
__________________
2 / 2 a*cos(l)
pi*a * / a - ----------- *sin(f)
\/ -4 + cos(l)
-----------------------------------
(6 - 6*cos(l))*cos(f)
$$\frac{\pi a^{2} \sqrt{a^{2} - \frac{a \cos{\left(l \right)}}{\cos{\left(l \right)} - 4}} \sin{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}$$
pi*a^2*sqrt(a^2 - a*cos(l)/(-4 + cos(l)))*sin(f)/((6 - 6*cos(l))*cos(f))