Let the inner product on $P_4$ be with respect to $x_1 = 1$, $x_2 = -1$, $x_3 = 2$, and $x_4 = -2$. Find the angle between

$$p(x) = 1+x+x^{2}+x^{3}$$

and

$$q(x) = x-1+x^{2}-x^{3}.$$

Determine the vector projection of $p$ onto $q$. Use asin() or acos() to enter arcsine and arccosine and the projection should be a polynomial in the variable $x$.

Angle:

Projection: