1809.sagews

ЗАВДАННЯ 2

ДЛЯ ПРАВИЛЬНОГО ВИКОНАННЯ ПРИКЛАДІВ НЕОБХІДНО ВИПРАВИТИ ПОМИЛКИ, ДОПУЩЕНІ У ПРОГРАМНИХ КОДАХ!

№2.2.1. Обчислити $|-(-5)|$.

|-(-5)|

Syntax Error: |-(-5)|

№2.2.2. Обчислити значення тригонометричних функцій: $\sin2$, $\sin^{2}{π}$, $\sin{π}$, $\cos \frac{π}{4}$, $tg{π}$, $ctg \frac{π}{2}$.

sin2

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/10.py", line 6, in <module> exec compile(ur'sin2' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> NameError: name 'sin2' is not defined

sin^2(pi)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/11.py", line 6, in <module> exec compile(ur'sin**Integer(2)(pi)' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> TypeError: 'sage.rings.integer.Integer' object is not callable

Sin(pi)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/12.py", line 6, in <module> exec compile(ur'Sin(pi)' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> NameError: name 'Sin' is not defined

cos(Pi/4)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/13.py", line 6, in <module> exec compile(ur'cos(Pi/Integer(4))' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> NameError: name 'Pi' is not defined

tg(pi)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/27.py", line 6, in <module> exec compile(ur'tg(pi)' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> NameError: name 'tg' is not defined

ctg(pi/2)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/1.py", line 6, in <module> exec compile(ur'ctg(pi/Integer(2))' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> NameError: name 'ctg' is not defined

№2.2.3. Вивести числове значення константи ${π}$.

pi

\pi

№2.2.4. Обчислити $5!$ (факторіал числа 5).

n=5
n!

Syntax Error: n!

№2.2.5. Обчислити значення виразу $a+b$, якщо:
а) $a=3$ та $b=5$;
б) $a=2$ та $b=5,7$.

a=3 b=5
a+b

Syntax Error: a=3 b=5

a=2
b=5,7
a+b

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/notebook/sage_notebook/worksheets/admin/33/code/20.py", line 8, in <module> exec compile(ur'a+b' + '\n', '', 'single') File "/usr/local/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module> File "element.pyx", line 713, in sage.structure.element.ModuleElement.__add__ File "coerce.pyx", line 295, in sage.structure.coerce.CoercionModel_cache_maps.bin_op_c TypeError: unsupported operand parent(s) for '+': 'Integer Ring' and '<type 'tuple'>'

№2.2.6. Обчислити:
а) ${\sqrt{1 + \sqrt{1 + \sqrt{1+\sqrt{2}}}}}$;
б) ${\frac{ 1-\sqrt{3} }{2+\sqrt{7}}}$;
в) ${\left(1 + \sqrt{5} \right)}^{\frac{2}{3}}$.
(Отримані результати мають бути представлені у вигляді десяткових дробів.)

sqrt(1+sqrt(1+sqrt(1+sqrt(2))))

sqrt(sqrt(sqrt(sqrt(2) + 1) + 1) + 1)

1-sqrt(3)/2+sqrt(7)

\sqrt{ 7 } - \frac{\sqrt{ 3 }}{2} + 1

(1+sqrt(5))^2/3

\frac{{\left( \sqrt{ 5 } + 1 \right)}^{2} }{3}