Тригонометрическая часть
[src] / pi x\
-2*csc|45 + -- - -|
\ 2 2/
------------------------------------
/ 2/ pi x\\
| csc |45 + -- - -||
| \ 2 2/| / x\
|1 + -----------------|*csc|-45 + -|
| 2/ x\ | \ 2/
| csc |-45 + -| |
\ \ 2/ /
−(1+csc2(2x−45)csc2(−2x+2π+45))csc(2x−45)2csc(−2x+2π+45) / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
| / x\
| -2*tan|-45 + -|
< \ 2/
|----------------- otherwise
| 2/ x\
|1 + tan |-45 + -|
\ \ 2/
⎩⎨⎧0−tan2(2x−45)+12tan(2x−45)forim(x)=0∧(−x−28π+90)modπ=0otherwise 2/ x\
-4*sin |-45 + -|
\ 2/
----------------------------------
/ 4/ x\\
| 4*sin |-45 + -||
| \ 2/|
|1 + ---------------|*sin(-90 + x)
| 2 |
\ sin (-90 + x) /
−(sin2(x−90)4sin4(2x−45)+1)sin(x−90)4sin2(2x−45) / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
| // 0 for And(im(x) = 0, (-90 + x + 29*pi) mod pi = 0)\
| || |
| || / x\ |
< || 2*cot|-45 + -| |
|-|< \ 2/ | otherwise
| ||----------------- otherwise |
| || 2/ x\ |
| ||1 + cot |-45 + -| |
\ \\ \ 2/ /
⎩⎨⎧0−⎩⎨⎧0cot2(2x−45)+12cot(2x−45)forim(x)=0∧(x−90+29π)modπ=0otherwiseforim(x)=0∧(−x−28π+90)modπ=0otherwise -1
-----------------
/ pi\
sec|-90 + x - --|
\ 2 /
−sec(x−90−2π)1 / x\ / x\
-2*sec|-45 + -|*sin|-45 + -|
\ 2/ \ 2/
----------------------------
2/ x\
1 + tan |-45 + -|
\ 2/
−tan2(2x−45)+12sin(2x−45)sec(2x−45) // 0 for And(im(x) = 0, (-90 + x + 29*pi) mod pi = 0)\
|| |
|| / x\ |
|| 2*cot|-45 + -| |
-|< \ 2/ |
||----------------- otherwise |
|| 2/ x\ |
||1 + cot |-45 + -| |
\\ \ 2/ /
−⎩⎨⎧0cot2(2x−45)+12cot(2x−45)forim(x)=0∧(x−90+29π)modπ=0otherwise / pi\
-cos|-90 + x - --|
\ 2 /
−cos(x−90−2π) −sin(x−90) / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
| / x\
| -2*cot|-45 + -|
< \ 2/
|----------------- otherwise
| 2/ x\
|1 + cot |-45 + -|
\ \ 2/
⎩⎨⎧0−cot2(2x−45)+12cot(2x−45)forim(x)=0∧(−x−28π+90)modπ=0otherwise / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
< // 0 for And(im(x) = 0, (-90 + x + 29*pi) mod pi = 0)\
|-|< | otherwise
\ \\sin(-90 + x) otherwise /
⎩⎨⎧0−{0sin(x−90)forim(x)=0∧(x−90+29π)modπ=0otherwiseforim(x)=0∧(−x−28π+90)modπ=0otherwise / pi\
cos|90 - x - --|
\ 2 /
cos(−x−2π+90) // 0 for And(im(x) = 0, (-90 + x + 29*pi) mod pi = 0)\
-|< |
\\sin(-90 + x) otherwise /
−{0sin(x−90)forim(x)=0∧(x−90+29π)modπ=0otherwise / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
| -1
<----------------- otherwise
| / pi\
|sec|-90 + x - --|
\ \ 2 /
{0−sec(x−90−2π)1forim(x)=0∧(−x−28π+90)modπ=0otherwise / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
< -1
|------------ otherwise
\csc(-90 + x)
{0−csc(x−90)1forim(x)=0∧(−x−28π+90)modπ=0otherwise / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
|
< / pi\
|-cos|-90 + x - --| otherwise
\ \ 2 /
{0−cos(x−90−2π)forim(x)=0∧(−x−28π+90)modπ=0otherwise 1
----------------
/ pi\
sec|90 - x - --|
\ 2 /
sec(−x−2π+90)1 / 0 for And(im(x) = 0, (90 - x - 28*pi) mod pi = 0)
<
\-sin(-90 + x) otherwise
{0−sin(x−90)forim(x)=0∧(−x−28π+90)modπ=0otherwise -2
--------------------------------
/ 1 \ / x\
|1 + -------------|*cot|-45 + -|
| 2/ x\| \ 2/
| cot |-45 + -||
\ \ 2//
−(1+cot2(2x−45)1)cot(2x−45)2 / x pi\
-2*cos|-45 + - - --|
\ 2 2 /
-------------------------------------
/ 2/ x pi\\
| cos |-45 + - - --||
| \ 2 2 /| / x\
|1 + ------------------|*cos|-45 + -|
| 2/ x\ | \ 2/
| cos |-45 + -| |
\ \ 2/ /
−(1+cos2(2x−45)cos2(2x−45−2π))cos(2x−45)2cos(2x−45−2π) / x\ / x\
- tan|-45 + -| - cos(-90 + x)*tan|-45 + -|
\ 2/ \ 2/
−cos(x−90)tan(2x−45)−tan(2x−45) / x\
-2*sec|-45 + -|
\ 2/
------------------------------------------
/ 2/ x\ \
| sec |-45 + -| |
| \ 2/ | / x pi\
|1 + ------------------|*sec|-45 + - - --|
| 2/ x pi\| \ 2 2 /
| sec |-45 + - - --||
\ \ 2 2 //
−(sec2(2x−45−2π)sec2(2x−45)+1)sec(2x−45−2π)2sec(2x−45) -1
------------
csc(-90 + x)
−csc(x−90)1 / x\
-2*tan|-45 + -|
\ 2/
-----------------
2/ x\
1 + tan |-45 + -|
\ 2/
−tan2(2x−45)+12tan(2x−45)