How do you convert $r = 5 cos (t)$ $r = 5 cos (t)$ to rectangular form?

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How do you convert $r = 5 cos (t)$ $r = 5 cos (t)$ to rectangular form?

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Answer 1 · 2016-03-03T17:33:51

$r = 5 cos t \to r \cdot r = r \cdot 5 cos t \to r^{2} = 5 r cos t \to x^{2} + y^{2} = 5 x \to x^{2} - 5 x + y^{2} = 0 \to {(x - \frac{5}{2})}^{2} + y^{2} = \frac{25}{4}$ $r=5cost->r*r=r*5cost->r^2=5rcost->x^2+y^2=5x->x^2-5x+y^2=0->(x-5/2)^2+y^2=25/4$

Explanation:

Multiply both sides by r then use the formula $r^{2} = x^{2} + y^{2}, x = r cos θ$ $r^2=x^2+y^2, x=rcostheta$ to change from polar to rectangular. Put everything on one side and complete the square to find the answer.

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How do you convert $r = 5 cos (t)$ $r = 5 cos (t)$ to rectangular form?

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How do you convert r = 5 cos (t)r=5cos(t)r = 5 cos (t) to rectangular form?

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Explanation:

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How do you convert $r = 5 cos (t)$ $r = 5 cos (t)$ to rectangular form?