Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- sin(-t)/tan(-t)-cos(2*pi+t) если t=-2
- b^2-4*b*y/2*y^2-b*y-4*y/b-2*y если y=-3/2
- 7*a/6*c-49*a^2+36*c^2/42+6*c-49*a/7*a если a=2
- x*2-1 если x=2
- Разложить многочлен на множители:
- 16*a^2-56*a*b+49*b^2
- x^2+4*x+3
- 4*z*b+11*z^n-28*b-77*n
- a^8-1
- Общий знаменатель:
- (sin(pi)/16*cos(pi)^(3)/16-sin(pi)^(3)/16*cos(pi)/16)
- 5*z/4*c+3*z+z-6*c/3*c+z
- a^3+2*a^2+8/a^2+8/a^3
- x^2/(13*a+x)-169*a^2/(13*a+x)
- Умножение столбиком:
- 32*28
- 45*19
- 56*20
- 70*43
- Деление столбиком:
- 2100/6
- 3256/6
- 7281/9
- 87100/2931
- Раскрыть скобки в:
- x*(-6)*(x+3)
- (n+2)^2+(n+2)*(n-2)+n-2^2
- (x^2-25)*(x+4)
- 4*x^2+19*x-5
- Разложение числа на простые множители:
- 25698
- 12545
- 204
- 24848
- График функции y =:
- -2
- Производная:
- -2
- Интеграл d{x}:
-
-2
-
Идентичные выражения
- sin(-t)/tan(-t)-cos(два *pi+t) если t=- два
- синус от ( минус t) делить на тангенс от ( минус t) минус косинус от (2 умножить на число пи плюс t) если t равно минус 2
- синус от ( минус t) делить на тангенс от ( минус t) минус косинус от (два умножить на число пи плюс t) если t равно минус два
- sin(-t)/tan(-t)-cos(2pi+t) если t=-2
- sin-t/tan-t-cos2pi+t если t=-2
- sin(-t)/tan(-t)-cos(2*pi+t) при t=-2
- sin(-t) разделить на tan(-t)-cos(2*pi+t) если t=-2
-
Похожие выражения
- sin(-t)/tan(t)-cos(2*pi+t) если t=-2
- sin(-t)/tan(-t)+cos(2*pi+t) если t=-2
- sin(-t)/tan(-t)-cos(2*pi+t) если t=+2
- sin(-t)/tan(-t)-cos(2*pi-t) если t=-2
- sin(t)/tan(-t)-cos(2*pi+t) если t=-2
-
Что Вы имели ввиду?
- sin(-t)/(tan(-t) - cos(2*pi + t))
- sin(-t)/(tan(-t) - cos(2*pi) + t)
- sin(-t)/(tan(-t) - cos(2)*pi + t)
- sin(-t)*(2*pi + t)/(tan(-t) - cos(t))
- sin(-t)/tan(-t) - cos(2*pi + t)
- sin(-t)*(-t)/tan(t) - cos(2*pi + t)
- sin(-t)*(-t)/tan(t) - cos(2*pi + t)
sin(-t)/tan(-t)-cos(2*pi+t) если t=-2
Решение
Вы ввели
[src]
sin(-t) ------- - cos(2*pi + t) tan(-t)
$$- \cos{\left(t + 2 \pi \right)} + \frac{\sin{\left(- t \right)}}{\tan{\left(- t \right)}}$$
sin(-t)/tan(-t) - cos(2*pi + t)
Общий знаменатель
[src]
sin(-t)
-cos(t) + -------
tan(-t)
$$- \cos{\left(t \right)} + \frac{\sin{\left(- t \right)}}{\tan{\left(- t \right)}}$$
-cos(t) + sin(-t)/tan(-t)
Рациональный знаменатель
[src]
sin(t)
-cos(t) + ------
tan(t)
$$- \cos{\left(t \right)} + \frac{\sin{\left(t \right)}}{\tan{\left(t \right)}}$$
-cos(t)*tan(t) + sin(t)
-----------------------
tan(t)
$$\frac{- \cos{\left(t \right)} \tan{\left(t \right)} + \sin{\left(t \right)}}{\tan{\left(t \right)}}$$
(-cos(t)*tan(t) + sin(t))/tan(t)
Объединение рациональных выражений
[src]
-cos(t)*tan(t) + sin(t)
-----------------------
tan(t)
$$\frac{- \cos{\left(t \right)} \tan{\left(t \right)} + \sin{\left(t \right)}}{\tan{\left(t \right)}}$$
(-cos(t)*tan(t) + sin(t))/tan(t)
Степени
[src]
sin(t)
-cos(t) + ------
tan(t)
$$- \cos{\left(t \right)} + \frac{\sin{\left(t \right)}}{\tan{\left(t \right)}}$$
I*(t + 2*pi) I*(-t - 2*pi) / I*t -I*t\ / I*t -I*t\
e e \- e + e /*\e + e /
- ------------- - -------------- - -------------------------------
2 2 / -I*t I*t\
2*\- e + e /
$$- \frac{\left(- e^{i t} + e^{- i t}\right) \left(e^{i t} + e^{- i t}\right)}{2 \left(e^{i t} - e^{- i t}\right)} - \frac{e^{i \left(- t - 2 \pi\right)}}{2} - \frac{e^{i \left(t + 2 \pi\right)}}{2}$$
-exp(i*(t + 2*pi))/2 - exp(i*(-t - 2*pi))/2 - (-exp(i*t) + exp(-i*t))*(exp(i*t) + exp(-i*t))/(2*(-exp(-i*t) + exp(i*t)))
Комбинаторика
[src]
-(-sin(t) + cos(t)*tan(t))
---------------------------
tan(t)
$$- \frac{\cos{\left(t \right)} \tan{\left(t \right)} - \sin{\left(t \right)}}{\tan{\left(t \right)}}$$
-(-sin(t) + cos(t)*tan(t))/tan(t)
Тригонометрическая часть
[src]
0
$$0$$
2/t\
1 - 2*cos |-| + cos(t)
\2/
$$- 2 \cos^{2}{\left(\frac{t}{2} \right)} + \cos{\left(t \right)} + 1$$
sin(t)
-cos(t) + ------
tan(t)
$$- \cos{\left(t \right)} + \frac{\sin{\left(t \right)}}{\tan{\left(t \right)}}$$
sin(2*t)
-cos(t) + --------
2*sin(t)
$$- \cos{\left(t \right)} + \frac{\sin{\left(2 t \right)}}{2 \sin{\left(t \right)}}$$
1 csc(t) - ------ + ---------- sec(t) 2*csc(2*t)
$$\frac{\csc{\left(t \right)}}{2 \csc{\left(2 t \right)}} - \frac{1}{\sec{\left(t \right)}}$$
/ pi\ sin(2*t)
- sin|t + --| + --------
\ 2 / 2*sin(t)
$$- \sin{\left(t + \frac{\pi}{2} \right)} + \frac{\sin{\left(2 t \right)}}{2 \sin{\left(t \right)}}$$
/ pi\
cos|2*t - --|
\ 2 /
-cos(t) + -------------
/ pi\
2*cos|t - --|
\ 2 /
$$- \cos{\left(t \right)} + \frac{\cos{\left(2 t - \frac{\pi}{2} \right)}}{2 \cos{\left(t - \frac{\pi}{2} \right)}}$$
/ pi\
sec|t - --|
1 \ 2 /
- ------ + ---------------
sec(t) / pi\
2*sec|2*t - --|
\ 2 /
$$\frac{\sec{\left(t - \frac{\pi}{2} \right)}}{2 \sec{\left(2 t - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(t \right)}}$$
/ 2 \
| 1 cos (t)| /t\
-cos(t) + |------ + -------|*tan|-|
\tan(t) sin(t)/ \2/
$$\left(\frac{\cos^{2}{\left(t \right)}}{\sin{\left(t \right)}} + \frac{1}{\tan{\left(t \right)}}\right) \tan{\left(\frac{t}{2} \right)} - \cos{\left(t \right)}$$
2/t\ /t\
1 - tan |-| 2*tan|-|
\2/ \2/
- ----------- + --------------------
2/t\ / 2/t\\
1 + tan |-| |1 + tan |-||*tan(t)
\2/ \ \2//
$$- \frac{- \tan^{2}{\left(\frac{t}{2} \right)} + 1}{\tan^{2}{\left(\frac{t}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{t}{2} \right)}}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right) \tan{\left(t \right)}}$$
1
1 - -------
2/t\
cot |-|
\2/ 2*cot(t)
- ----------- + --------------------
1 / 1 \ /t\
1 + ------- |1 + -------|*cot|-|
2/t\ | 2/t\| \2/
cot |-| | cot |-||
\2/ \ \2//
$$- \frac{1 - \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}} + \frac{2 \cot{\left(t \right)}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}\right) \cot{\left(\frac{t}{2} \right)}}$$
/ 0 for t mod pi = 0
<
// 1 for t mod 2*pi = 0\ \sin(t) otherwise
- |< | + -------------------------
\\cos(t) otherwise / tan(t)
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\cos{\left(t \right)} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\sin{\left(t \right)} & \text{otherwise} \end{cases}}{\tan{\left(t \right)}}\right)$$
// 1 for t mod 2*pi = 0\ // 0 for t mod pi = 0\ - |< | + |< |*cot(t) \\cos(t) otherwise / \\sin(t) otherwise /
$$\left(\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\sin{\left(t \right)} & \text{otherwise} \end{cases}\right) \cot{\left(t \right)}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\cos{\left(t \right)} & \text{otherwise} \end{cases}\right)$$
/t pi\ / 2/t\\
2*tan|- + --| |1 + tan |-||*tan(t)
\2 4 / \ \2//
- ---------------- + ----------------------
2/t pi\ / 2 \ /t\
1 + tan |- + --| 2*\1 + tan (t)/*tan|-|
\2 4 / \2/
$$\frac{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right) \tan{\left(t \right)}}{2 \left(\tan^{2}{\left(t \right)} + 1\right) \tan{\left(\frac{t}{2} \right)}} - \frac{2 \tan{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1}$$
2/t\
4*sin |-|*cos(t)
2*(-1 - cos(2*t) + 2*cos(t)) \2/
- ------------------------------ + -------------------
2 2 4/t\
1 - cos(2*t) + 2*(1 - cos(t)) sin (t) + 4*sin |-|
\2/
$$\frac{4 \sin^{2}{\left(\frac{t}{2} \right)} \cos{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)} + \sin^{2}{\left(t \right)}} - \frac{2 \cdot \left(2 \cos{\left(t \right)} - \cos{\left(2 t \right)} - 1\right)}{2 \left(- \cos{\left(t \right)} + 1\right)^{2} - \cos{\left(2 t \right)} + 1}$$
/ 0 for t mod pi = 0
|
|1 - cos(t)
<---------- otherwise
| /t\
| tan|-|
// 1 for t mod 2*pi = 0\ \ \2/
- |< | + -----------------------------
\\cos(t) otherwise / tan(t)
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\cos{\left(t \right)} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{- \cos{\left(t \right)} + 1}{\tan{\left(\frac{t}{2} \right)}} & \text{otherwise} \end{cases}}{\tan{\left(t \right)}}\right)$$
// 0 for t mod pi = 0\ // 1 for t mod 2*pi = 0\ |< |*sin(2*t) || | \\sin(t) otherwise / - |< / pi\ | + ------------------------------------ ||sin|t + --| otherwise | 2 \\ \ 2 / / 2*sin (t)
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\sin{\left(t + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\sin{\left(t \right)} & \text{otherwise} \end{cases}\right) \sin{\left(2 t \right)}}{2 \sin^{2}{\left(t \right)}}\right)$$
// 0 for t mod pi = 0\
|| |
|< / pi\ |*cos(t)
||cos|t - --| otherwise |
// 1 for t mod 2*pi = 0\ \\ \ 2 / /
- |< | + ---------------------------------------
\\cos(t) otherwise / / pi\
cos|t - --|
\ 2 /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\cos{\left(t - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \cos{\left(t \right)}}{\cos{\left(t - \frac{\pi}{2} \right)}}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\cos{\left(t \right)} & \text{otherwise} \end{cases}\right)$$
// 0 for t mod pi = 0\
|| |
|| 1 | / pi\
|<----------- otherwise |*sec|t - --|
|| / pi\ | \ 2 /
// 1 for t mod 2*pi = 0\ ||sec|t - --| |
|| | \\ \ 2 / /
- |< 1 | + --------------------------------------------
||------ otherwise | sec(t)
\\sec(t) /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{1}{\sec{\left(t - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \sec{\left(t - \frac{\pi}{2} \right)}}{\sec{\left(t \right)}}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(t \right)}} & \text{otherwise} \end{cases}\right)$$
4/t\
4*sin |-|
\2/
1 - --------- 2/t\
2 2*sin |-|*sin(2*t)
sin (t) \2/
- ------------- + -----------------------
4/t\ / 4/t\\
4*sin |-| | 4*sin |-||
\2/ | \2/| 3
1 + --------- |1 + ---------|*sin (t)
2 | 2 |
sin (t) \ sin (t) /
$$- \frac{- \frac{4 \sin^{4}{\left(\frac{t}{2} \right)}}{\sin^{2}{\left(t \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{t}{2} \right)}}{\sin^{2}{\left(t \right)}} + 1} + \frac{2 \sin^{2}{\left(\frac{t}{2} \right)} \sin{\left(2 t \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{t}{2} \right)}}{\sin^{2}{\left(t \right)}} + 1\right) \sin^{3}{\left(t \right)}}$$
// 0 for t mod pi = 0\
|| |
// 1 for t mod 2*pi = 0\ |< 1 |*csc(t)
|| | ||------ otherwise |
|| 1 | \\csc(t) /
- |<----------- otherwise | + ----------------------------------
|| /pi \ | /pi \
||csc|-- - t| | csc|-- - t|
\\ \2 / / \2 /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{1}{\csc{\left(t \right)}} & \text{otherwise} \end{cases}\right) \csc{\left(t \right)}}{\csc{\left(- t + \frac{\pi}{2} \right)}}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- t + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
/ 0 for t mod pi = 0
|
| /t\
| 2*tan|-|
< \2/
// 1 for t mod 2*pi = 0\ |----------- otherwise
|| | | 2/t\
|| 2/t\ | |1 + tan |-|
||1 - tan |-| | \ \2/
- |< \2/ | + ------------------------------
||----------- otherwise | tan(t)
|| 2/t\ |
||1 + tan |-| |
\\ \2/ /
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{t}{2} \right)} + 1}{\tan^{2}{\left(\frac{t}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1} & \text{otherwise} \end{cases}}{\tan{\left(t \right)}}\right)$$
// 1 for t mod 2*pi = 0\ // 0 for t mod pi = 0\ || | || | || 2/t\ | || /t\ | ||-1 + cot |-| | || 2*cot|-| | - |< \2/ | + |< \2/ |*cot(t) ||------------ otherwise | ||----------- otherwise | || 2/t\ | || 2/t\ | ||1 + cot |-| | ||1 + cot |-| | \\ \2/ / \\ \2/ /
$$\left(\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \cot{\left(t \right)}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for t mod 2*pi = 0\ // 0 for t mod pi = 0\
|| | || |
- |
$$\left(\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\sin{\left(t \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \cot{\left(t \right)}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\cos{\left(t \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
/ 0 for t mod pi = 0
|
| 2
// 1 for t mod 2*pi = 0\ |-------------------- otherwise
|| |
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} \right)}}} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} \right)}}\right) \tan{\left(\frac{t}{2} \right)}} & \text{otherwise} \end{cases}}{\tan{\left(t \right)}}\right)$$
2/t pi\
cos |- - --|
\2 2 /
1 - ------------
2/t\ /t pi\
cos |-| 2*cos(t)*cos|- - --|
\2/ \2 2 /
- ---------------- + -------------------------------------
2/t pi\ / 2/t pi\\
cos |- - --| | cos |- - --||
\2 2 / | \2 2 /| /t\ / pi\
1 + ------------ |1 + ------------|*cos|-|*cos|t - --|
2/t\ | 2/t\ | \2/ \ 2 /
cos |-| | cos |-| |
\2/ \ \2/ /
$$- \frac{1 - \frac{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} \right)}}} + \frac{2 \cos{\left(t \right)} \cos{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} \right)}}\right) \cos{\left(\frac{t}{2} \right)} \cos{\left(t - \frac{\pi}{2} \right)}}$$
2/t\
sec |-|
\2/
1 - ------------
2/t pi\ /t\ / pi\
sec |- - --| 2*sec|-|*sec|t - --|
\2 2 / \2/ \ 2 /
- ---------------- + -------------------------------------
2/t\ / 2/t\ \
sec |-| | sec |-| |
\2/ | \2/ | /t pi\
1 + ------------ |1 + ------------|*sec(t)*sec|- - --|
2/t pi\ | 2/t pi\| \2 2 /
sec |- - --| | sec |- - --||
\2 2 / \ \2 2 //
$$- \frac{- \frac{\sec^{2}{\left(\frac{t}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{t}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1} + \frac{2 \sec{\left(\frac{t}{2} \right)} \sec{\left(t - \frac{\pi}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{t}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(t \right)} \sec{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}$$
2/pi t\
csc |-- - -|
\2 2/
1 - ------------
2/t\ /pi t\
csc |-| 2*csc(t)*csc|-- - -|
\2/ \2 2/
- ---------------- + -------------------------------------
2/pi t\ / 2/pi t\\
csc |-- - -| | csc |-- - -||
\2 2/ | \2 2/| /t\ /pi \
1 + ------------ |1 + ------------|*csc|-|*csc|-- - t|
2/t\ | 2/t\ | \2/ \2 /
csc |-| | csc |-| |
\2/ \ \2/ /
$$- \frac{1 - \frac{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{t}{2} \right)}}}{1 + \frac{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{t}{2} \right)}}} + \frac{2 \csc{\left(t \right)} \csc{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{t}{2} \right)}}\right) \csc{\left(\frac{t}{2} \right)} \csc{\left(- t + \frac{\pi}{2} \right)}}$$
// zoo for t mod pi = 0\
// 0 for 2*t mod pi = 0\ || |
// / pi\ \ |< |*|< 1 |
|| 0 for |t + --| mod pi = 0| \\sin(2*t) otherwise / ||------ otherwise |
|| \ 2 / | \\sin(t) /
- |< | + -----------------------------------------------------------
|| /t pi\ | 2
||(1 + sin(t))*cot|- + --| otherwise |
\\ \2 4 / /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\sin{\left(2 t \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: t \bmod \pi = 0 \\\frac{1}{\sin{\left(t \right)}} & \text{otherwise} \end{cases}\right)}{2}\right) - \left(\begin{cases} 0 & \text{for}\: \left(t + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(t \right)} + 1\right) \cot{\left(\frac{t}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)$$
/ 0 for t mod pi = 0
|
| 2*(-sin(2*t) + 2*sin(t))
<------------------------------ otherwise
// 1 for t mod 2*pi = 0\ | 2
|| | |1 - cos(2*t) + 2*(1 - cos(t))
|| 2 | \
- |< -4 + 4*sin (t) + 4*cos(t) | + -------------------------------------------------
||--------------------------- otherwise | tan(t)
|| 2 2 |
\\2*(1 - cos(t)) + 2*sin (t) /
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{4 \sin^{2}{\left(t \right)} + 4 \cos{\left(t \right)} - 4}{2 \left(- \cos{\left(t \right)} + 1\right)^{2} + 2 \sin^{2}{\left(t \right)}} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \cdot \left(2 \sin{\left(t \right)} - \sin{\left(2 t \right)}\right)}{2 \left(- \cos{\left(t \right)} + 1\right)^{2} - \cos{\left(2 t \right)} + 1} & \text{otherwise} \end{cases}}{\tan{\left(t \right)}}\right)$$
// 1 for t mod 2*pi = 0\ // 0 for t mod pi = 0\ || | || | ||/ 1 for t mod 2*pi = 0 | ||/ 0 for t mod pi = 0 | ||| | ||| | ||| 2/t\ | ||| /t\ | - |<|-1 + cot |-| | + |<| 2*cot|-| |*cot(t) ||< \2/ otherwise | ||< \2/ otherwise | |||------------ otherwise | |||----------- otherwise | ||| 2/t\ | ||| 2/t\ | |||1 + cot |-| | |||1 + cot |-| | \\\ \2/ / \\\ \2/ /
$$\left(\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \cot{\left(t \right)}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 0 for t mod pi = 0\
|| |
|| sin(t) |
||----------------------- otherwise |
// 1 for t mod 2*pi = 0\ ||/ 2 \ |
|| | |<| sin (t) | 2/t\ |*sin(2*t)
|| 2 | |||1 + ---------|*sin |-| |
|| sin (t) | ||| 4/t\| \2/ |
||-1 + --------- | ||| 4*sin |-|| |
|| 4/t\ | ||\ \2// |
|| 4*sin |-| | \\ /
- |< \2/ | + -----------------------------------------------------
||-------------- otherwise | 2
|| 2 | 2*sin (t)
|| sin (t) |
||1 + --------- |
|| 4/t\ |
|| 4*sin |-| |
\\ \2/ /
$$\left(- \begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)}}}{1 + \frac{\sin^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)}}} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{\sin{\left(t \right)}}{\left(1 + \frac{\sin^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)}}\right) \sin^{2}{\left(\frac{t}{2} \right)}} & \text{otherwise} \end{cases}\right) \sin{\left(2 t \right)}}{2 \sin^{2}{\left(t \right)}}\right)$$
// zoo for t mod pi = 0\
// 0 for 2*t mod pi = 0\ || |
|| | || 2/t\ |
|| 2*cot(t) | ||1 + cot |-| |
// / pi\ \ |<----------- otherwise |*|< \2/ |
|| 0 for |t + --| mod pi = 0| || 2 | ||----------- otherwise |
|| \ 2 / | ||1 + cot (t) | || /t\ |
|| | \\ / || 2*cot|-| |
|| /t pi\ | \\ \2/ /
- |< 2*cot|- + --| | + -------------------------------------------------------------------
|| \2 4 / | 2
||---------------- otherwise |
|| 2/t pi\ |
||1 + cot |- + --| |
\\ \2 4 / /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \cot{\left(t \right)}}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: t \bmod \pi = 0 \\\frac{\cot^{2}{\left(\frac{t}{2} \right)} + 1}{2 \cot{\left(\frac{t}{2} \right)}} & \text{otherwise} \end{cases}\right)}{2}\right) - \left(\begin{cases} 0 & \text{for}\: \left(t + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for t mod pi = 0\
|| |
|| /t\ |
|| 2*cos|-| |
|| \2/ |
// 1 for t mod 2*pi = 0\ ||------------------------------ otherwise |
|| | |
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{t}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{t}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \cos{\left(t \right)}}{\cos{\left(t - \frac{\pi}{2} \right)}}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{t}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{t}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for t mod pi = 0\
|| |
|| /t pi\ |
|| 2*sec|- - --| |
|| \2 2 / |
// 1 for t mod 2*pi = 0\ ||------------------------- otherwise | / pi\
|| | |
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} \right)}}\right) \sec{\left(\frac{t}{2} \right)}} & \text{otherwise} \end{cases}\right) \sec{\left(t - \frac{\pi}{2} \right)}}{\sec{\left(t \right)}}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 0 for t mod pi = 0\
|| |
|| /t\ |
|| 2*csc|-| |
|| \2/ |
// 1 for t mod 2*pi = 0\ ||------------------------------ otherwise |
|| | |
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: t \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{t}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{t}{2} \right)}}{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \csc{\left(t \right)}}{\csc{\left(- t + \frac{\pi}{2} \right)}}\right) - \left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{t}{2} \right)}}{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{t}{2} \right)}}{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
-Piecewise((1, Mod(t = 2*pi, 0)), ((-1 + csc(t/2)^2/csc(pi/2 - t/2)^2)/(1 + csc(t/2)^2/csc(pi/2 - t/2)^2), True)) + Piecewise((0, Mod(t = pi, 0)), (2*csc(t/2)/((1 + csc(t/2)^2/csc(pi/2 - t/2)^2)*csc(pi/2 - t/2)), True))*csc(t)/csc(pi/2 - t)