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### Cartesian equation for $((\sin\theta)^3+\cos\theta,(\cos\theta)^3+\sin\theta)$

To find a polynomial $P(x,y)$ such that: $$P\left(\sin^3\theta+\cos\theta,\,\cos^3\theta+\sin\theta\right) = 0 \quad \quad \forall\,\theta \in [0,2\pi)$$ there are at least two automated approaches. ...
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Generally when considering AP's with 3,4,5 terms respectively, it makes it easier if we write the terms as: (which makes calculating terms of the AP much faster(especially sum and product) ) $3: a-... • 737 1 vote ### System of equations on$\mathbb R$I don’t know why you equate$\Delta$to zero. Instead, at that juncture, you could have easily apply Cramer's rule as shown below.$$x=\dfrac{ \begin{bmatrix} 12 & -4& t \\ 3 & t & 4 \\... • 3,493 1 vote ### Cartesian equation for$((\sin\theta)^3+\cos\theta,(\cos\theta)^3+\sin\theta)$The Maple function eliminate() eliminates the parameter immediately: ... • 89.4k 1 vote ### Cartesian equation for$((\sin\theta)^3+\cos\theta,(\cos\theta)^3+\sin\theta)$An experimental answer, in need of explanations : I used Geogebra for sketching the initial curve (green curve above). It is made of 2 symmetric arcs, one obtained for$\theta \in [0,\pi)$, the other ... • 74.9k 1 vote Accepted ### Given x, y are real number that are not equal to 1. Find all x, y that satisfy: The resultant of the two polynomials$f=x^8+y^7-x(1+y^7)$and$g=y^8+x^7-y(1+x^7)$is given by a polynomial in$x$, which has four real roots, namely$x=0,1,-1$and$x=0.502017055178$, which is the ... • 125k 1 vote Accepted ### Solving a system of linear equations involving tensors This system is linear for$D_{i,j}$variables. there are$n^2$variables and$n^2$equations so you can solve it with changing this to linear system. you should just rearrange matrix notations in$M_{...
Once you have defined $S_1$, $S_2$ and $M$, you can forget the fact that you have a matrix. It will not give you any more structure. Now, Rodrigo is right in that your system of equations are ...