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8.2.4 – Rewriting Polar Equations

8.2.4 – Rewriting Polar Equations. We talked extensively about converting rectangular to polar equations Use the substitutions; x = rcos ( ϴ ) y = rsin ( ϴ ) x 2 + y 2 = r 2 t an( ϴ ) = y/x Now, we will take something in terms or r and ϴ , and try to get back in terms of x and y.

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8.2.4 – Rewriting Polar Equations

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  1. 8.2.4 – Rewriting Polar Equations

  2. We talked extensively about converting rectangular to polar equations • Use the substitutions; • x = rcos(ϴ) • y = rsin(ϴ) • x2 + y2 = r2 • tan(ϴ) = y/x • Now, we will take something in terms or r and ϴ, and try to get back in terms of x and y

  3. Conversion • In order to convert back to rectangular, we will need to try and isolate everything similar to the substitutions used before • IE, try and rewrite so we could possibly have an rcos(ϴ) or rsin(ϴ) in the equation

  4. Key • Sometimes, if we are missing a particular factor, we may have to multiply both sides by a factor of r • Example. If I 2cos(ϴ) = 3r, if we multiply both sides by r, we would have 2rcos(ϴ) = 3r2

  5. Example. Convert the equation r = 5cos(ϴ) from polar to rectangular.

  6. Example. Convert the polar equation 2r = sec(ϴ) from polar to rectangular.

  7. Example. Convert the polar equation ϴ = π/6 to rectangular.

  8. Example. Convert the polar equation r = 7 from polar to rectangular. (hint: think about squaring both sides)

  9. Assignment • Pg. 629 • 31-40 all

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