Convert Equations Between Polar and Rectangular Forms definitions Flashcards
Convert Equations Between Polar and Rectangular Forms definitions
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Rectangular Form An equation format using x and y variables, commonly representing Cartesian coordinates in the plane. Polar Form An equation format using r and theta, representing points based on distance from the origin and angle from the positive x-axis. r The distance from the origin to a point in the polar coordinate system. Theta The angle measured from the positive x-axis to a point in the polar coordinate system. r Cosine Theta An expression equivalent to the x-coordinate in rectangular form when converting between coordinate systems. r Sine Theta An expression equivalent to the y-coordinate in rectangular form when converting between coordinate systems. r Squared An expression representing the sum of the squares of x and y, or the squared distance from the origin. Cosecant Theta The reciprocal of sine theta, often used when expressing polar equations with y in rectangular form. Secant Theta The reciprocal of cosine theta, used in polar equations to facilitate conversion to rectangular form. Completing the Square An algebraic technique used to rewrite quadratic equations, often to identify conic sections like circles. Standard Form A recognizable equation format, such as x squared plus y squared equals a constant, that reveals the graph's shape. Circle A set of points equidistant from a center, represented by equations like x squared plus y squared equals a constant. Graph Shape The geometric figure represented by an equation, such as a line or circle, after conversion between forms. Algebraic Manipulation The process of rearranging and transforming equations to facilitate conversion between coordinate systems. Trigonometric Function A mathematical function like sine, cosine, or their reciprocals, used to relate polar and rectangular variables.
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