Sinusoidal series
=================

A sinusoidal series is defined as:

   .. math::

      \begin{array}{l}
      x_0 = 1 \\
      x_{i+1} = 2 \sin x_i+ 3 \cos x_i, i>=0
      \end{array}

This sequence begins with two positive terms and continues with
negative terms. The first 10 values (rounded to 2 decimals) are: 1,
3.30, -3.28, -2.69, -3.57, -1.89, -2.83, -3.47 -2.21 -3.39.

Save both functions into file ``sinusoidal.py``.

#. Write the function :py:func:`sinusoidal1` that given an integer
   :math:`k`, computes the sum of the elements of the previous series to
   the *kth* term (included), that is, :math:`x_0 +x_1 +...+x_k`. Examples:

   .. literalinclude:: test-sinusoidal1.txt
      :language: python3
      :lines: 3-
             
   .. note::

      You can download the file with tests :download:`test-sinusoidal1.txt <test-sinusoidal1.txt>`

     
#. Write the function :py:func:`sinusoidal2` that given a real value
   ``smax``, tolerance ``epsilon``, returns the position of the term in
   the previous series that is equal to the given ``value`` with tolerance
   ``epsilon``. To determine the equality between two real numbers you
   must check if the absolute value of the difference between them is
   less than epsilon.  Examples:

   .. literalinclude:: test-sinusoidal2.txt
      :language: python3
      :lines: 3-
             
   .. note::

      You can download the file with tests :download:`test-sinusoidal2.txt <test-sinusoidal2.txt>`

.. rubric:: Solution
               
A solution of these functions is provided in file :download:`sinusoidal.py <solutions/sinusoidal.py>`