1. The problem statement, all variables and given/known data Show that the following nonlinear system has 18 solutions if: 0 ≤ α ≤ 2∏ 0 ≤ β ≤ 2∏ 0 ≤ γ ≤ 2∏ sin(α) + 2cos(β) + 3tan(γ) = 0 2sin(α) + 5cos(β) + 3tan(γ) = 0 -sin(α) -5cos(β) + 5tan(γ) = 0 using the substitutions x = sin(α) y = cos(β) z = tan(γ) 3. The attempt at a solution I went ahead and substituted and got: x + 2y + 3z = 0 2x + 5y + 3z = 0 -x -5y + 5z = 0 and put it into an augmented matrix with the coefficients on one side and the constants on the other. I also tried computing the values at 0 and 2∏ using the substitution, giving me: [ 0 2 0 | 0 ] [ 0 5 0 | 0 ] [ 0 -5 0 | 0 ] for both values, and I got 16 more matrices for all the other values that I use with these functions, I seem to be missing one. What i'm thinking about, though: don't they all contain the trivial solution? How are they each different in their own way? Thanks for your help, PF.