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Convert Equations Between Polar and Rectangular Forms quiz

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  • What substitutions do you use for x and y when converting a rectangular equation to polar form?
    Replace x with r*cos(theta) and y with r*sin(theta).
  • How do you convert the equation y = 5 into polar form?
    Replace y with r*sin(theta), solve for r, and get r = 5*csc(theta).
  • What is the polar form of the equation y = x + 1?
    It is r = 1 / (sin(theta) - cos(theta)).
  • How do you convert x^2 + y^2 = 25 into polar form?
    Replace x^2 + y^2 with r^2 to get r^2 = 25, then r = 5.
  • What does the equation r = 5 represent in rectangular form?
    It represents a circle with radius 5 centered at the origin.
  • When converting from polar to rectangular form, what should you try to get in your equation?
    Try to get terms like r*cos(theta), r*sin(theta), or r^2.
  • How do you convert r = 4 into rectangular form?
    Square both sides to get r^2 = 16, then substitute x^2 + y^2 for r^2 to get x^2 + y^2 = 16.
  • What is the rectangular form of r = sec(theta)?
    Rewrite sec(theta) as 1/cos(theta), multiply both sides by cos(theta) to get r*cos(theta) = 1, then substitute x for r*cos(theta) to get x = 1.
  • How do you convert r = 6*sin(theta) into rectangular form?
    Multiply both sides by r to get r^2 = 6r*sin(theta), then substitute x^2 + y^2 for r^2 and y for r*sin(theta) to get x^2 + y^2 = 6y.
  • What algebraic technique is used to rewrite x^2 + y^2 = 6y into a standard form?
    Complete the square on the y terms to get x^2 + (y - 3)^2 = 9.
  • What shape does the equation x^2 + (y - 3)^2 = 9 represent?
    It represents a circle of radius 3 centered at (0, 3).
  • What is the rectangular form of r*cos(theta) = 1?
    It is x = 1.
  • What should you do if your polar equation contains a fraction with a trigonometric denominator?
    Multiply both sides by the denominator to eliminate the fraction.
  • What is the general strategy for converting polar equations to rectangular form?
    Manipulate the equation to get r*cos(theta), r*sin(theta), or r^2, then substitute x, y, or x^2 + y^2, respectively.
  • Why is it helpful to identify the shape of the graph when converting equations?
    Recognizing the shape helps confirm the equation is in a standard or recognizable form.