SOLUTION: solve for all values of θ for = the < 360 degrees, that satisfy the equation sec ^2 θ - 3=tan θ , to the nearest tenth of a degree
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Question 310783: solve for all values of θ for = the < 360 degrees, that satisfy the equation sec ^2 θ - 3=tan θ , to the nearest tenth of a degree Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! solve for all values of θ for = the < 360 degrees, that satisfy the equation sec ^2 θ - 3=tan θ , to the nearest tenth of a degree
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sec^2(x) - 3 = tan(x)
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Note: sec^2(x) = tan^2(x) + 1
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tan^2(x) + 1 - 3 = tan(x)
Rearrange:
tan^2(x) - tan(x) -2 = 0
Factor:
(tan(x)-2)(tan(x)+1) = 0
tan(x) = 2 or tan(x) = -1
x = 63.43 degrees or x = 63.43+180 = 243.43 degrees
x = 135 degrees or x = 315 degrees
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Cheers,
Stan H.
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