Question

Find all solutions of the equation in the interval [0,2pi) algebraically. Use the table feature of a graphing utility to check your answers numerically.

sin^2x + cos x + 1=0

Answer 1

This is a quadratic factoring problem, just with sin and cos. Well, you need to have all the terms be in either sin or cos. In this case its easier to turn sin^2(x) into cosines. If you know about the pythagorean identity of

\[\sin ^{2}x + \cos ^{2}x = 1\]
then you can use that equation and solve for sin^2(x).

Once you solve for sin^2(x), you can substitute it into your equation and then we can go from there.