Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- (2*i-j)*j+(j-2*k)*k+(i-2*k)^2 если i=3
- 8*x-17*x-19+21*x если x=-1
- cos(2*a)*cos(2*(2*pi+a))-3-sin(a)^22 если a=-3/2
- sin(2*t)+2*cos(2*t)-1 если t=-4
- Разложить многочлен на множители:
- 3*x^2-24*x*y+48*y^2
- 16*x^2+40*x+25
- 8+a^3
- -y^2-y^2
- Общий знаменатель:
- 5/a+5-a^2+25/a^2-25-5/5-a
- (x+5)/(x+7)+14/(x+14)
- (w^2)/(w+10)+(20*w+100)/(w+10)
- t2/t+9+18*t+81/t+9
- Умножение столбиком:
- 18*27
- 96*53
- 22*52
- 23*34
- Деление столбиком:
- 1535/5
- 882/7
- 96/9
- 1648/8
- Раскрыть скобки в:
- 6*y*(y-1)-(3-y)^2
- 3*x^2*7*x
- 19*(-a+b-c)
- (x-a)*(x-b)*(x-c)+(x-d)*((x-a)*(x-b)+(x-c)*(-a-b+2*x))
- Разложение числа на простые множители:
- 6468
- 2722
- 216
- 4620
- Производная:
- -4
- Интеграл d{x}:
-
-4
- График функции y =:
- -4
-
Идентичные выражения
- sin(два *t)+ два *cos(два *t)- один если t=- четыре
- синус от (2 умножить на t) плюс 2 умножить на косинус от (2 умножить на t) минус 1 если t равно минус 4
- синус от (два умножить на t) плюс два умножить на косинус от (два умножить на t) минус один если t равно минус четыре
- sin(2t)+2cos(2t)-1 если t=-4
- sin2t+2cos2t-1 если t=-4
- sin(2*t)+2*cos(2*t)-1 при t=-4
-
Похожие выражения
- sin(2*t)+2*cos(2*t)+1 если t=-4
- sin(2*t)+2*cos(2*t)-1 если t=+4
- sin(2*t)-2*cos(2*t)-1 если t=-4
sin(2*t)+2*cos(2*t)-1 если t=-4
Решение
Вы ввели
[src]
sin(2*t) + 2*cos(2*t) - 1
$$\sin{\left(2 t \right)} + 2 \cos{\left(2 t \right)} - 1$$
sin(2*t) + 2*cos(2*t) - 1*1
Подстановка условия
[src]
sin(2*t) + 2*cos(2*t) - 1*1 при t = -4
подставляем
sin(2*t) + 2*cos(2*t) - 1
$$\sin{\left(2 t \right)} + 2 \cos{\left(2 t \right)} - 1$$
-1 + 2*cos(2*t) + sin(2*t)
$$\sin{\left(2 t \right)} + 2 \cos{\left(2 t \right)} - 1$$
переменные
t = -4
$$t = -4$$
-1 + 2*cos(2*(-4)) + sin(2*(-4))
$$\sin{\left(2 (-4) \right)} + 2 \cos{\left(2 (-4) \right)} - 1$$
-1 - sin(8) + 2*cos(8)
$$-1 - \sin{\left(8 \right)} + 2 \cos{\left(8 \right)}$$
-1 - sin(8) + 2*cos(8)
Степени
[src]
/ -2*I*t 2*I*t\
I*\- e + e / -2*I*t 2*I*t
-1 - ---------------------- + e + e
2
$$e^{2 i t} - \frac{i \left(e^{2 i t} - e^{- 2 i t}\right)}{2} - 1 + e^{- 2 i t}$$
-1 - i*(-exp(-2*i*t) + exp(2*i*t))/2 + exp(-2*i*t) + exp(2*i*t)
Тригонометрическая часть
[src]
2 -3 + 4*cos (t) + sin(2*t)
$$4 \cos^{2}{\left(t \right)} + \sin{\left(2 t \right)} - 3$$
/pi \
-1 + 2*sin|-- + 2*t| + sin(2*t)
\2 /
$$\sin{\left(2 t \right)} + 2 \sin{\left(2 t + \frac{\pi}{2} \right)} - 1$$
/ pi\
-1 + 2*cos(2*t) + cos|2*t - --|
\ 2 /
$$2 \cos{\left(2 t \right)} + \cos{\left(2 t - \frac{\pi}{2} \right)} - 1$$
1 2
-1 + -------- + --------
csc(2*t) sec(2*t)
$$-1 + \frac{2}{\sec{\left(2 t \right)}} + \frac{1}{\csc{\left(2 t \right)}}$$
1 2
-1 + ------------- + --------
/ pi\ sec(2*t)
sec|2*t - --|
\ 2 /
$$-1 + \frac{1}{\sec{\left(2 t - \frac{\pi}{2} \right)}} + \frac{2}{\sec{\left(2 t \right)}}$$
1 2
-1 + -------- + -------------
csc(2*t) /pi \
csc|-- - 2*t|
\2 /
$$-1 + \frac{2}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 t \right)}}$$
1 2
-1 + ------------- + --------
/pi \ sec(2*t)
sec|-- - 2*t|
\2 /
$$-1 + \frac{1}{\sec{\left(- 2 t + \frac{\pi}{2} \right)}} + \frac{2}{\sec{\left(2 t \right)}}$$
1 2
-1 + ------------- + -------------
csc(pi - 2*t) /pi \
csc|-- - 2*t|
\2 /
$$-1 + \frac{2}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- 2 t + \pi \right)}}$$
2 2 -1 - 2*sin (t) + 2*cos (t) + 2*cos(t)*sin(t)
$$- 2 \sin^{2}{\left(t \right)} + 2 \sin{\left(t \right)} \cos{\left(t \right)} + 2 \cos^{2}{\left(t \right)} - 1$$
/ 2 \
2*\1 - tan (t)/ 2*tan(t)
-1 + --------------- + -----------
2 2
1 + tan (t) 1 + tan (t)
$$\frac{2 \cdot \left(- \tan^{2}{\left(t \right)} + 1\right)}{\tan^{2}{\left(t \right)} + 1} - 1 + \frac{2 \tan{\left(t \right)}}{\tan^{2}{\left(t \right)} + 1}$$
/ pi\
4*tan|t + --|
2*tan(t) \ 4 /
-1 + ----------- + ----------------
2 2/ pi\
1 + tan (t) 1 + tan |t + --|
\ 4 /
$$-1 + \frac{4 \tan{\left(t + \frac{\pi}{4} \right)}}{\tan^{2}{\left(t + \frac{\pi}{4} \right)} + 1} + \frac{2 \tan{\left(t \right)}}{\tan^{2}{\left(t \right)} + 1}$$
/ pi\
4*tan|t + --|
2*cot(t) \ 4 /
-1 + ----------- + ----------------
2 2/ pi\
1 + cot (t) 1 + tan |t + --|
\ 4 /
$$-1 + \frac{2 \cot{\left(t \right)}}{\cot^{2}{\left(t \right)} + 1} + \frac{4 \tan{\left(t + \frac{\pi}{4} \right)}}{\tan^{2}{\left(t + \frac{\pi}{4} \right)} + 1}$$
2/ pi\
-1 + tan |t + --| / 2 \
\ 4 / 2*\-1 + cot (t)/
-1 + ----------------- + ----------------
2/ pi\ 2
1 + tan |t + --| 1 + cot (t)
\ 4 /
$$\frac{\tan^{2}{\left(t + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(t + \frac{\pi}{4} \right)} + 1} + \frac{2 \left(\cot^{2}{\left(t \right)} - 1\right)}{\cot^{2}{\left(t \right)} + 1} - 1$$
2/ pi\
1 - cot |t + --| / 2 \
\ 4 / 2*\1 - tan (t)/
-1 + ---------------- + ---------------
2/ pi\ 2
1 + cot |t + --| 1 + tan (t)
\ 4 /
$$\frac{2 \cdot \left(- \tan^{2}{\left(t \right)} + 1\right)}{\tan^{2}{\left(t \right)} + 1} + \frac{- \cot^{2}{\left(t + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(t + \frac{\pi}{4} \right)} + 1} - 1$$
/ 1 \
2*|1 - -------|
| 2 |
2 \ cot (t)/
-1 + -------------------- + ---------------
/ 1 \ 1
|1 + -------|*cot(t) 1 + -------
| 2 | 2
\ cot (t)/ cot (t)
$$\frac{2 \cdot \left(1 - \frac{1}{\cot^{2}{\left(t \right)}}\right)}{1 + \frac{1}{\cot^{2}{\left(t \right)}}} - 1 + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(t \right)}}\right) \cot{\left(t \right)}}$$
// 1 for t mod pi = 0\ // 0 for 2*t mod pi = 0\
-1 + 2*|< | + |< |
\\cos(2*t) otherwise / \\sin(2*t) otherwise /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\sin{\left(2 t \right)} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\cos{\left(2 t \right)} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 0 for 2*t mod pi = 0\
// 1 for t mod pi = 0\ || |
-1 + 2*|< | + |< / pi\ |
\\cos(2*t) otherwise / ||cos|2*t - --| otherwise |
\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\cos{\left(2 t - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\cos{\left(2 t \right)} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\
|| | // 0 for 2*t mod pi = 0\
-1 + 2*|< /pi \ | + |< |
||sin|-- + 2*t| otherwise | \\sin(2*t) otherwise /
\\ \2 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\sin{\left(2 t \right)} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\sin{\left(2 t + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) - 1$$
// /pi \ \
|| 0 for |-- + 2*t| mod pi = 0| // 0 for 2*t mod pi = 0\
-1 + 2*|< \2 / | + |< |
|| | \\sin(2*t) otherwise /
\\cos(2*t) otherwise /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\sin{\left(2 t \right)} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 0 & \text{for}\: \left(2 t + \frac{\pi}{2}\right) \bmod \pi = 0 \\\cos{\left(2 t \right)} & \text{otherwise} \end{cases}\right)\right) - 1$$
// / 3*pi\ \
// 1 for t mod pi = 0\ || 1 for |2*t + ----| mod 2*pi = 0|
-1 + 2*|< | + |< \ 2 / |
\\cos(2*t) otherwise / || |
\\sin(2*t) otherwise /
$$\left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\cos{\left(2 t \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\begin{cases} 1 & \text{for}\: \left(2 t + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(2 t \right)} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 2*t mod pi = 0\
// 1 for t mod pi = 0\ || |
|| | || 1 |
-1 + 2*|< 1 | + |<------------- otherwise |
||-------- otherwise | || / pi\ |
\\sec(2*t) / ||sec|2*t - --| |
\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{1}{\sec{\left(2 t - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{1}{\sec{\left(2 t \right)}} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\
|| | // 0 for 2*t mod pi = 0\
|| 1 | || |
-1 + 2*|<------------- otherwise | + |< 1 |
|| /pi \ | ||-------- otherwise |
||csc|-- - 2*t| | \\csc(2*t) /
\\ \2 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{1}{\csc{\left(2 t \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{1}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - 1$$
/ 4 \
| 4*sin (t)|
2*|1 - ---------|
| 2 | 2
\ sin (2*t)/ 4*sin (t)
-1 + ----------------- + ------------------------
4 / 4 \
4*sin (t) | 4*sin (t)|
1 + --------- |1 + ---------|*sin(2*t)
2 | 2 |
sin (2*t) \ sin (2*t)/
$$\frac{2 \left(- \frac{4 \sin^{4}{\left(t \right)}}{\sin^{2}{\left(2 t \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(t \right)}}{\sin^{2}{\left(2 t \right)}} + 1} - 1 + \frac{4 \sin^{2}{\left(t \right)}}{\left(\frac{4 \sin^{4}{\left(t \right)}}{\sin^{2}{\left(2 t \right)}} + 1\right) \sin{\left(2 t \right)}}$$
// 1 for t mod pi = 0\ // 0 for 2*t mod pi = 0\
|| | || |
|| 2 | || 2*cot(t) |
-1 + 2*|<-1 + cot (t) | + |<----------- otherwise |
||------------ otherwise | || 2 |
|| 2 | ||1 + cot (t) |
\\1 + cot (t) / \\ /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \cot{\left(t \right)}}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{\cot^{2}{\left(t \right)} - 1}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\ // 0 for 2*t mod pi = 0\
|| | || |
|| 2 | || 2*tan(t) |
-1 + 2*|<1 - tan (t) | + |<----------- otherwise |
||----------- otherwise | || 2 |
|| 2 | ||1 + tan (t) |
\\1 + tan (t) / \\ /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \tan{\left(t \right)}}{\tan^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{- \tan^{2}{\left(t \right)} + 1}{\tan^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - 1$$
/ 2 \
| sec (t) |
2*|1 - ------------|
| 2/ pi\|
| sec |t - --||
\ \ 2 // 2*sec(t)
-1 + -------------------- + ------------------------------
2 / 2 \
sec (t) | sec (t) | / pi\
1 + ------------ |1 + ------------|*sec|t - --|
2/ pi\ | 2/ pi\| \ 2 /
sec |t - --| | sec |t - --||
\ 2 / \ \ 2 //
$$\frac{2 \left(- \frac{\sec^{2}{\left(t \right)}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + 1\right)}{\frac{\sec^{2}{\left(t \right)}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + 1} - 1 + \frac{2 \sec{\left(t \right)}}{\left(\frac{\sec^{2}{\left(t \right)}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(t - \frac{\pi}{2} \right)}}$$
/ 2/ pi\\
| cos |t - --||
| \ 2 /|
2*|1 - ------------| / pi\
| 2 | 2*cos|t - --|
\ cos (t) / \ 2 /
-1 + -------------------- + -------------------------
2/ pi\ / 2/ pi\\
cos |t - --| | cos |t - --||
\ 2 / | \ 2 /|
1 + ------------ |1 + ------------|*cos(t)
2 | 2 |
cos (t) \ cos (t) /
$$\frac{2 \cdot \left(1 - \frac{\cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t \right)}}\right)}{1 + \frac{\cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t \right)}}} - 1 + \frac{2 \cos{\left(t - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t \right)}}\right) \cos{\left(t \right)}}$$
/ 2/pi \\
| csc |-- - t||
| \2 /|
2*|1 - ------------| /pi \
| 2 | 2*csc|-- - t|
\ csc (t) / \2 /
-1 + -------------------- + -------------------------
2/pi \ / 2/pi \\
csc |-- - t| | csc |-- - t||
\2 / | \2 /|
1 + ------------ |1 + ------------|*csc(t)
2 | 2 |
csc (t) \ csc (t) /
$$\frac{2 \cdot \left(1 - \frac{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}}{\csc^{2}{\left(t \right)}}\right)}{1 + \frac{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}}{\csc^{2}{\left(t \right)}}} - 1 + \frac{2 \csc{\left(- t + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}}{\csc^{2}{\left(t \right)}}\right) \csc{\left(t \right)}}$$
// 1 for t mod pi = 0\
|| | // 0 for 2*t mod pi = 0\
|| 1 | || |
||-1 + ------- | || 2 |
|| 2 | ||-------------------- otherwise |
-1 + 2*|< tan (t) | + |
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(t \right)}}\right) \tan{\left(t \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(t \right)}}}{1 + \frac{1}{\tan^{2}{\left(t \right)}}} & \text{otherwise} \end{cases}\right)\right) - 1$$
// /pi \ \
|| 0 for |-- + 2*t| mod pi = 0|
|| \2 / | // 0 for 2*t mod pi = 0\
|| | || |
|| / pi\ | || 2*cot(t) |
-1 + 2*|< 2*cot|t + --| | + |<----------- otherwise |
|| \ 4 / | || 2 |
||---------------- otherwise | ||1 + cot (t) |
|| 2/ pi\ | \\ /
||1 + cot |t + --| |
\\ \ 4 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \cot{\left(t \right)}}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 0 & \text{for}\: \left(2 t + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(t + \frac{\pi}{4} \right)}}{\cot^{2}{\left(t + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - 1$$
// / 3*pi\ \
|| 1 for |2*t + ----| mod 2*pi = 0|
// 1 for t mod pi = 0\ || \ 2 / |
|| | || |
|| 2 | || 2/ pi\ |
-1 + 2*|<-1 + cot (t) | + |<-1 + tan |t + --| |
||------------ otherwise | || \ 4 / |
|| 2 | ||----------------- otherwise |
\\1 + cot (t) / || 2/ pi\ |
|| 1 + tan |t + --| |
\\ \ 4 / /
$$\left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{\cot^{2}{\left(t \right)} - 1}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + \left(\begin{cases} 1 & \text{for}\: \left(2 t + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(t + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(t + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod pi = 0\ // 0 for 2*t mod pi = 0\
|| | || |
-1 + 2*|
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\sin{\left(2 t \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\cos{\left(2 t \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\
|| |
|| 2 | // 0 for 2*t mod pi = 0\
|| sin (2*t) | || |
||-1 + --------- | || sin(2*t) |
|| 4 | ||----------------------- otherwise |
-1 + 2*|< 4*sin (t) | + |
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{\sin{\left(2 t \right)}}{\left(1 + \frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{4}{\left(t \right)}}\right) \sin^{2}{\left(t \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{4}{\left(t \right)}}}{1 + \frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{4}{\left(t \right)}}} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\ // 0 for 2*t mod pi = 0\
|| | || |
||/ 1 for t mod pi = 0 | ||/ 0 for 2*t mod pi = 0 |
||| | ||| |
-1 + 2*|<| 2 | + |<| 2*cot(t) |
||<-1 + cot (t) otherwise | ||<----------- otherwise otherwise |
|||------------ otherwise | ||| 2 |
||| 2 | |||1 + cot (t) |
\\\1 + cot (t) / \\\ /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \cot{\left(t \right)}}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{\cot^{2}{\left(t \right)} - 1}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\
|| |
|| 2 | // 0 for 2*t mod pi = 0\
|| cos (t) | || |
||-1 + ------------ | || 2*cos(t) |
|| 2/ pi\ | ||------------------------------ otherwise |
|| cos |t - --| | ||/ 2 \ |
-1 + 2*|< \ 2 / | + |<| cos (t) | / pi\ |
||----------------- otherwise | |||1 + ------------|*cos|t - --| |
|| 2 | ||| 2/ pi\| \ 2 / |
|| cos (t) | ||| cos |t - --|| |
|| 1 + ------------ | ||\ \ 2 // |
|| 2/ pi\ | \\ /
|| cos |t - --| |
\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \cos{\left(t \right)}}{\left(\frac{\cos^{2}{\left(t \right)}}{\cos^{2}{\left(t - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(t - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{\frac{\cos^{2}{\left(t \right)}}{\cos^{2}{\left(t - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(t \right)}}{\cos^{2}{\left(t - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\
|| | // 0 for 2*t mod pi = 0\
|| 2/ pi\ | || |
|| sec |t - --| | || / pi\ |
|| \ 2 / | || 2*sec|t - --| |
||-1 + ------------ | || \ 2 / |
|| 2 | ||------------------------- otherwise |
-1 + 2*|< sec (t) | + |
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \sec{\left(t - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\sec^{2}{\left(t \right)}}\right) \sec{\left(t \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\sec^{2}{\left(t \right)}}}{1 + \frac{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\sec^{2}{\left(t \right)}}} & \text{otherwise} \end{cases}\right)\right) - 1$$
// 1 for t mod pi = 0\
|| |
|| 2 | // 0 for 2*t mod pi = 0\
|| csc (t) | || |
||-1 + ------------ | || 2*csc(t) |
|| 2/pi \ | ||------------------------------ otherwise |
|| csc |-- - t| | ||/ 2 \ |
-1 + 2*|< \2 / | + |<| csc (t) | /pi \ |
||----------------- otherwise | |||1 + ------------|*csc|-- - t| |
|| 2 | ||| 2/pi \| \2 / |
|| csc (t) | ||| csc |-- - t|| |
|| 1 + ------------ | ||\ \2 // |
|| 2/pi \ | \\ /
|| csc |-- - t| |
\\ \2 / /
$$\left(\begin{cases} 0 & \text{for}\: 2 t \bmod \pi = 0 \\\frac{2 \csc{\left(t \right)}}{\left(\frac{\csc^{2}{\left(t \right)}}{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- t + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(2 \left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{\frac{\csc^{2}{\left(t \right)}}{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(t \right)}}{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)\right) - 1$$
-1 + 2*Piecewise((1, Mod(t = pi, 0)), ((-1 + csc(t)^2/csc(pi/2 - t)^2)/(1 + csc(t)^2/csc(pi/2 - t)^2), True)) + Piecewise((0, Mod(2*t = pi, 0)), (2*csc(t)/((1 + csc(t)^2/csc(pi/2 - t)^2)*csc(pi/2 - t)), True))