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Trigonometry

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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?

  • Trigonometry - ,

    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

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