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Convert the polar equation to rectangular coordinates.

sec(θ)=2

Guest May 7, 2017
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 #1
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Solved it smiley

 

Initial Question:

\(sec(\theta )=2\)

 

Convert it to cosine

\(cos(\theta)=\frac{1}{2}\)

Which means

\(\theta = \pm \frac{\pi}{3}\)

\(tan(\theta)=\pm\frac{\sqrt{3}}{1}=\pm\sqrt{3}\)

\(\frac{y}{x}=\pm\sqrt{3}\)

Final answer is.

\(y=\pm\sqrt{3}x\)

Guest May 7, 2017
 #2
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sec(θ)=2

 

r/x  = 2

 

sqrt [ x^2 + y^2] / x  = 2

 

sqrt [ x^2 + y^2 ]  = 2x     square both sides

 

x^2 + y^2  = 4x^2

 

y^2  = 3x^2         take the square root of both sides

 

y =  ±√(3)x

 

 

cool cool cool

CPhill  May 7, 2017

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