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# trig

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sin^2(x) + cos(x) + 1 = 0 In the interval [0, 2π)

Guest Jun 1, 2017
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sin^2(x) + cos(x) + 1 = 0 In the interval [0, 2π)

$$sin^2(x) + cos(x) + 1 = 0 \\ -cos^2(x) + cos(x) + 2= 0\\ cos^2(x) - cos(x) - 2= 0\\ let\;\;t=cos(x)\\ t^2-t-2=0\\ (t-2)(t+1)=0\\ t=2\;\;or\;\;t=-1\\ -1\le t \le 1\\ so\;\; t=-1\\ cos(x)=-1\\ x=\pi$$

Melody  Jun 1, 2017

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