Convert the equation to polar form. (use variables r and θ as needed.) x = y

Solution:

Consider the following diagram,

We can see that the relationship between rectangular and polar coordinates are:

\(r=\sqrt{x^{2}+y^{2}}\)

\(\theta =arctan(\frac{y}{x})\)

Converting to polar coordinates,

\(x=rcos(\theta )\)

\(y=rsin(\theta )\)

Given, the equation x=y

So, \(rcos(\theta )=rsin(\theta )\)

\(cos(\theta )=sin(\theta )\)

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

We know, \(\frac{sin x}{cos x}=tan x\)

Therefore, the polar form of the equation is \(tan(\theta )=1\)

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Convert the equation to polar form. (use variables r and θ as needed.) x = y

Summary:

Converting the equation to polar form (use variables r and θ as needed.) x = y, we get \(tan(\theta)=1\).