Parte trigonométrica
[src]
/ /x \ /x\\
|cos|- - pi| + sin|-||
| \2 / \2/|
atan|--------------------|
| /x\ /x\ |
| - sin|-| + cos|-| |
\ \2/ \2/ /
atan ( sin ( x 2 ) + cos ( x 2 − π ) − sin ( x 2 ) + cos ( x 2 ) ) \operatorname{atan}{\left(\frac{\sin{\left(\frac{x}{2} \right)} + \cos{\left(\frac{x}{2} - \pi \right)}}{- \sin{\left(\frac{x}{2} \right)} + \cos{\left(\frac{x}{2} \right)}} \right)} atan ( − sin ( 2 x ) + cos ( 2 x ) sin ( 2 x ) + cos ( 2 x − π ) )
/ 1 1 \
|------ + -----------|
| /x\ /x \|
|csc|-| sec|- - pi||
| \2/ \2 /|
atan|--------------------|
| 1 1 |
| ------ - ------ |
| /x\ /x\ |
| sec|-| csc|-| |
\ \2/ \2/ /
atan ( 1 sec ( x 2 − π ) + 1 csc ( x 2 ) 1 sec ( x 2 ) − 1 csc ( x 2 ) ) \operatorname{atan}{\left(\frac{\frac{1}{\sec{\left(\frac{x}{2} - \pi \right)}} + \frac{1}{\csc{\left(\frac{x}{2} \right)}}}{\frac{1}{\sec{\left(\frac{x}{2} \right)}} - \frac{1}{\csc{\left(\frac{x}{2} \right)}}} \right)} atan s e c ( 2 x ) 1 − c s c ( 2 x ) 1 s e c ( 2 x − π ) 1 + c s c ( 2 x ) 1
/ 1 \
|-1 + ------------ |
| 2/pi x\ |
| cot |-- + -| |
| \4 4/ 2 |
|----------------- - ------------------------------|
| 1 / 1 \ /pi x\|
| 1 + ------------ |1 + ------------|*cot|-- + -||
| 2/pi x\ | 2/pi x\| \4 4/|
| cot |-- + -| | cot |-- + -|| |
| \4 4/ \ \4 4// |
atan|--------------------------------------------------|
| 2/pi x\ /pi x\ |
| -1 + cot |-- + -| 2*cot|-- + -| |
| \4 4/ \4 4/ |
| ----------------- + ---------------- |
| 2/pi x\ 2/pi x\ |
| 1 + cot |-- + -| 1 + cot |-- + -| |
\ \4 4/ \4 4/ /
atan ( − 1 + 1 cot 2 ( x 4 + π 4 ) 1 + 1 cot 2 ( x 4 + π 4 ) − 2 ( 1 + 1 cot 2 ( x 4 + π 4 ) ) cot ( x 4 + π 4 ) cot 2 ( x 4 + π 4 ) − 1 cot 2 ( x 4 + π 4 ) + 1 + 2 cot ( x 4 + π 4 ) cot 2 ( x 4 + π 4 ) + 1 ) \operatorname{atan}{\left(\frac{\frac{-1 + \frac{1}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}} - \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}\right) \cot{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}}{\frac{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} - 1}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1} + \frac{2 \cot{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1}} \right)} atan c o t 2 ( 4 x + 4 π ) + 1 c o t 2 ( 4 x + 4 π ) − 1 + c o t 2 ( 4 x + 4 π ) + 1 2 c o t ( 4 x + 4 π ) 1 + c o t 2 ( 4 x + 4 π ) 1 − 1 + c o t 2 ( 4 x + 4 π ) 1 − ( 1 + c o t 2 ( 4 x + 4 π ) 1 ) c o t ( 4 x + 4 π ) 2
/ 1 \
|1 - ------------ |
| 2/pi x\ |
| tan |-- + -| |
| \4 4/ 2 |
|---------------- - ------------------------------|
| 1 / 1 \ /pi x\|
|1 + ------------ |1 + ------------|*tan|-- + -||
| 2/pi x\ | 2/pi x\| \4 4/|
| tan |-- + -| | tan |-- + -|| |
| \4 4/ \ \4 4// |
atan|-------------------------------------------------|
| 2/pi x\ /pi x\ |
| 1 - tan |-- + -| 2*tan|-- + -| |
| \4 4/ \4 4/ |
| ---------------- + ---------------- |
| 2/pi x\ 2/pi x\ |
| 1 + tan |-- + -| 1 + tan |-- + -| |
\ \4 4/ \4 4/ /
atan ( 1 − 1 tan 2 ( x 4 + π 4 ) 1 + 1 tan 2 ( x 4 + π 4 ) − 2 ( 1 + 1 tan 2 ( x 4 + π 4 ) ) tan ( x 4 + π 4 ) 1 − tan 2 ( x 4 + π 4 ) tan 2 ( x 4 + π 4 ) + 1 + 2 tan ( x 4 + π 4 ) tan 2 ( x 4 + π 4 ) + 1 ) \operatorname{atan}{\left(\frac{\frac{1 - \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}} - \frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}\right) \tan{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}}{\frac{1 - \tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1}} \right)} atan t a n 2 ( 4 x + 4 π ) + 1 1 − t a n 2 ( 4 x + 4 π ) + t a n 2 ( 4 x + 4 π ) + 1 2 t a n ( 4 x + 4 π ) 1 + t a n 2 ( 4 x + 4 π ) 1 1 − t a n 2 ( 4 x + 4 π ) 1 − ( 1 + t a n 2 ( 4 x + 4 π ) 1 ) t a n ( 4 x + 4 π ) 2
/ 1 1 \
|------ - ------|
| /x\ /x\|
|csc|-| sec|-||
| \2/ \2/|
atan|---------------|
| 1 1 |
|------ - ------|
| /x\ /x\|
|sec|-| csc|-||
\ \2/ \2//
atan ( − 1 sec ( x 2 ) + 1 csc ( x 2 ) 1 sec ( x 2 ) − 1 csc ( x 2 ) ) \operatorname{atan}{\left(\frac{- \frac{1}{\sec{\left(\frac{x}{2} \right)}} + \frac{1}{\csc{\left(\frac{x}{2} \right)}}}{\frac{1}{\sec{\left(\frac{x}{2} \right)}} - \frac{1}{\csc{\left(\frac{x}{2} \right)}}} \right)} atan s e c ( 2 x ) 1 − c s c ( 2 x ) 1 − s e c ( 2 x ) 1 + c s c ( 2 x ) 1
/ /x\ /x\ \
| - cos|-| + sin|-| |
| \2/ \2/ |
atan|--------------------|
| /x\ / x\|
|cos|-| + sin|pi + -||
\ \2/ \ 2//
atan ( sin ( x 2 ) − cos ( x 2 ) sin ( x 2 + π ) + cos ( x 2 ) ) \operatorname{atan}{\left(\frac{\sin{\left(\frac{x}{2} \right)} - \cos{\left(\frac{x}{2} \right)}}{\sin{\left(\frac{x}{2} + \pi \right)} + \cos{\left(\frac{x}{2} \right)}} \right)} atan ( sin ( 2 x + π ) + cos ( 2 x ) sin ( 2 x ) − cos ( 2 x ) )
/ /x\ /x pi\\
|- cos|-| + cos|- - --||
| \2/ \2 2 /|
atan|----------------------|
| /x pi\ /x\|
|- cos|- - --| + cos|-||
\ \2 2 / \2//
atan ( − cos ( x 2 ) + cos ( x 2 − π 2 ) cos ( x 2 ) − cos ( x 2 − π 2 ) ) \operatorname{atan}{\left(\frac{- \cos{\left(\frac{x}{2} \right)} + \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)} - \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} \right)} atan ( cos ( 2 x ) − cos ( 2 x − 2 π ) − cos ( 2 x ) + cos ( 2 x − 2 π ) )
/ /pi x\ /x\\
|- sin|-- + -| + sin|-||
| \2 2/ \2/|
atan|----------------------|
| /x\ /pi x\|
|- sin|-| + sin|-- + -||
\ \2/ \2 2//
atan ( sin ( x 2 ) − sin ( x 2 + π 2 ) − sin ( x 2 ) + sin ( x 2 + π 2 ) ) \operatorname{atan}{\left(\frac{\sin{\left(\frac{x}{2} \right)} - \sin{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{- \sin{\left(\frac{x}{2} \right)} + \sin{\left(\frac{x}{2} + \frac{\pi}{2} \right)}} \right)} atan ( − sin ( 2 x ) + sin ( 2 x + 2 π ) sin ( 2 x ) − sin ( 2 x + 2 π ) )
/ 1 1 \
|----------- - ------|
| /pi x\ /x\|
|sec|-- - -| sec|-||
| \2 2/ \2/|
atan|--------------------|
| 1 1 |
|------ - -----------|
| /x\ /pi x\|
|sec|-| sec|-- - -||
\ \2/ \2 2//
atan ( 1 sec ( − x 2 + π 2 ) − 1 sec ( x 2 ) − 1 sec ( − x 2 + π 2 ) + 1 sec ( x 2 ) ) \operatorname{atan}{\left(\frac{\frac{1}{\sec{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(\frac{x}{2} \right)}}}{- \frac{1}{\sec{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{x}{2} \right)}}} \right)} atan − s e c ( − 2 x + 2 π ) 1 + s e c ( 2 x ) 1 s e c ( − 2 x + 2 π ) 1 − s e c ( 2 x ) 1
/ 2/pi x\ /pi x\ \
|-1 + tan |-- + -| 2*tan|-- + -| |
| \4 4/ \4 4/ |
|----------------- - ----------------|
| 2/pi x\ 2/pi x\|
| 1 + tan |-- + -| 1 + tan |-- + -||
| \4 4/ \4 4/|
atan|------------------------------------|
| 2/pi x\ /pi x\ |
|-1 + cot |-- + -| 2*cot|-- + -| |
| \4 4/ \4 4/ |
|----------------- + ----------------|
| 2/pi x\ 2/pi x\|
| 1 + cot |-- + -| 1 + cot |-- + -||
\ \4 4/ \4 4//
atan ( tan 2 ( x 4 + π 4 ) − 1 tan 2 ( x 4 + π 4 ) + 1 − 2 tan ( x 4 + π 4 ) tan 2 ( x 4 + π 4 ) + 1 cot 2 ( x 4 + π 4 ) − 1 cot 2 ( x 4 + π 4 ) + 1 + 2 cot ( x 4 + π 4 ) cot 2 ( x 4 + π 4 ) + 1 ) \operatorname{atan}{\left(\frac{\frac{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1}}{\frac{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} - 1}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1} + \frac{2 \cot{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1}} \right)} atan c o t 2 ( 4 x + 4 π ) + 1 c o t 2 ( 4 x + 4 π ) − 1 + c o t 2 ( 4 x + 4 π ) + 1 2 c o t ( 4 x + 4 π ) t a n 2 ( 4 x + 4 π ) + 1 t a n 2 ( 4 x + 4 π ) − 1 − t a n 2 ( 4 x + 4 π ) + 1 2 t a n ( 4 x + 4 π )
/ 1 1 \
|------ - -----------|
| /x\ /pi x\|
|csc|-| csc|-- - -||
| \2/ \2 2/|
atan|--------------------|
| 1 1 |
|----------- - ------|
| /pi x\ /x\|
|csc|-- - -| csc|-||
\ \2 2/ \2//
atan ( − 1 csc ( − x 2 + π 2 ) + 1 csc ( x 2 ) 1 csc ( − x 2 + π 2 ) − 1 csc ( x 2 ) ) \operatorname{atan}{\left(\frac{- \frac{1}{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(\frac{x}{2} \right)}}}{\frac{1}{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(\frac{x}{2} \right)}}} \right)} atan c s c ( − 2 x + 2 π ) 1 − c s c ( 2 x ) 1 − c s c ( − 2 x + 2 π ) 1 + c s c ( 2 x ) 1
/ 2/pi x\ /pi x\ \
|1 - cot |-- + -| 2*cot|-- + -| |
| \4 4/ \4 4/ |
|---------------- - ----------------|
| 2/pi x\ 2/pi x\|
|1 + cot |-- + -| 1 + cot |-- + -||
| \4 4/ \4 4/|
atan|-----------------------------------|
| 2/pi x\ /pi x\ |
|1 - tan |-- + -| 2*tan|-- + -| |
| \4 4/ \4 4/ |
|---------------- + ----------------|
| 2/pi x\ 2/pi x\|
|1 + tan |-- + -| 1 + tan |-- + -||
\ \4 4/ \4 4//
atan ( 1 − cot 2 ( x 4 + π 4 ) cot 2 ( x 4 + π 4 ) + 1 − 2 cot ( x 4 + π 4 ) cot 2 ( x 4 + π 4 ) + 1 1 − tan 2 ( x 4 + π 4 ) tan 2 ( x 4 + π 4 ) + 1 + 2 tan ( x 4 + π 4 ) tan 2 ( x 4 + π 4 ) + 1 ) \operatorname{atan}{\left(\frac{\frac{1 - \cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1} - \frac{2 \cot{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1}}{\frac{1 - \tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{4} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} + 1}} \right)} atan t a n 2 ( 4 x + 4 π ) + 1 1 − t a n 2 ( 4 x + 4 π ) + t a n 2 ( 4 x + 4 π ) + 1 2 t a n ( 4 x + 4 π ) c o t 2 ( 4 x + 4 π ) + 1 1 − c o t 2 ( 4 x + 4 π ) − c o t 2 ( 4 x + 4 π ) + 1 2 c o t ( 4 x + 4 π )
atan(((1 - cot(pi/4 + x/4)^2)/(1 + cot(pi/4 + x/4)^2) - 2*cot(pi/4 + x/4)/(1 + cot(pi/4 + x/4)^2))/((1 - tan(pi/4 + x/4)^2)/(1 + tan(pi/4 + x/4)^2) + 2*tan(pi/4 + x/4)/(1 + tan(pi/4 + x/4)^2)))