Sine function/Approximating polynomials/Various conditions/Exercise

{{ Mathematical text/Exercise{{{opt|}}} Let {{ Relationchain }} Determine polynomials {{mat|term= P,Q,R |pm=}} of degree {{mathl|term=  \leq 3 |pm=,}} fulfilling the following conditions.
 * Text=
 * f(x)
 * {{op:sin|x}}
 * pm=.
 * pm=.
 * pm=.
 * pm=.

(a) {{mat|term= P |pm=}} coincides with  at the points {{mathl|term= - \pi, 0, \pi |pm=.}}

(b) {{mat|term= Q |pm=}} coincides with  in {{mat|term=   0 |pm=}} and in {{mat|term=  \pi |pm=}} up to the first derivative.

(c) {{mat|term= R |pm=}}} coincides with {{mat|term= f |pm=}} in  up to the third derivative. }}
 * Textform=Exercise
 * Marks=8
 * m1=1
 * m2=4
 * m3=3