Trigonometry
posted by Veronica .
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