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Parametric Equations and Polar Coordinates

 Topic Review on "Title": Definition of parametric equations: Suppose that x and y are continuous functions of a third variable t. Then x=f(t) and y=g(t) are called parametric equations for the curve represented by (x,y). Lines in polar coordinates: Let and  then the polar equations of the lines x=a and y=b are and  for all values of

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 "Title" Tutorial Summary : Parametric equations are equations that are used to introduce polar coordinates and their relation with rectangular coordinates. Historic applications of parametric equations are discussed so the use of them is realized.   Polar coordinates simplified the work it takes to arrive at solutions in most trigonometry problems. Conversion between Cartesian coordinates and polar coordinate is important to determine the efficiency of them in trigonometric solutions. The graphs pf polar coordinates rely on the Cartesian coordinates and their properties.

 Tutorial Features: Specific Tutorial Features: • Several example problems with step by step illustrations of solutions. • Tables and graphs showing the Cartesian coordinates, polar coordinates and both of their properties. Series Features: • Concept map showing inter-connections of new concepts in this tutorial and those previously introduced. • Definition slides introduce terms as they are needed. • Visual representation of concepts • Animated examples—worked out step by step • A concise summary is given at the conclusion of the tutorial.

 "Title" Topic List: Parametric equations Parametric equations and their definitionPolar coordinates Polar coordinates and their definition Conversion between polar and Cartesian coordinatesPolar coordinates graphs Lines in polar coordinates Circles in polar coordinates

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