posted by Veronica on .
Okay, I have been given a trigonometric equation to solve (sin^2(theta) + cos(theta) = 2). So far, I have been able to use the Pythagorean identity to get (-cos^2(theta) + cos(theta) - 1 = 0), which I then multiplied by -1 on both sides to get: (cos^2(theta) - cos(theta) + 1 = 0). But, now I am stuck. I cannot figure out how to factor this equation from here. Does this equation have no solutions, or am I missing something?
sin^2 Ø = 1 - cos^ Ø
so replace that in the original to get
1 - cos^2Ø + cosØ - 2 = 0
cos^2Ø - cosØ + 1 = 0
It does not factor , so by the quadratic formula
cosØ = (1 ± √-3)/2
since the right side is a complex number there will be no solution for Ø