polar coordinates and polar graphs worksheet

#POLAR COORDINATES AND POLAR GRAPHS WORKSHEET SERIES#

Using the appropriate substitutions makes it possible to rewrite a polar equation as a rectangular equation, and then graph it in the rectangular plane.Transforming equations between polar and rectangular forms means making the appropriate substitutions based on the available formulas, together with algebraic manipulations.To convert from rectangular coordinates to polar coordinates, use one or more of the formulas:Ĭos θ = x r, sin θ = y r, tan θ = y x ,.To convert from polar coordinates to rectangular coordinates, use the formulas.Is negative, extend the directed line segment in the opposite direction of θ. Is negative, move in a clockwise direction, and extend a directed line segment the length of r Move in a counterclockwise direction from the polar axis by an angle of θ ,Īnd then extend a directed line segment from the pole the length of r

#POLAR COORDINATES AND POLAR GRAPHS WORKSHEET SERIES#

The polar grid is represented as a series of concentric circles radiating out from the pole, or origin.Comparing Polar and Rectangular CoordinatesĬos θ = x r → x = r cos θ sin θ = y r → y = r sin θ r 2 = x 2 + y 2 tan θ = y x.We can then use a graphing calculator to graph either the rectangular form or the polar form of the equation.Īccess these online resources for additional instruction and practice with polar coordinates. Since there are a number of polar equations that cannot be expressed clearly in Cartesian form, and vice versa, we can use the same procedures we used to convert points between the coordinate systems. Converting equations can be more difficult, but it can be beneficial to be able to convert between the two forms. We can now convert coordinates between polar and rectangular form. Transforming Equations between Polar and Rectangular Forms Is negative, we extend the directed line segment in the opposite direction, into the first quadrant. Is located in the third quadrant and, as r Indicates a move further counterclockwise by π , Will coincide with the original solution of ( 3 2, π 4 ). For example, the points ( − 3 2, 5 π 4 ) There are other sets of polar coordinates that will be the same as our first solution. Units in the counterclockwise direction and then a length of 2 from the pole. For example, to plot the point ( 2, π 4 ) , The polar point is written with the r-coordinate first. We move counterclockwise from the polar axis by an angle of θ ,Īnd measure a directed line segment the length of r Measured in radians, indicates the direction of r. Is the radius or length of the directed line segment from the pole. The polar grid is scaled as the unit circle with the positive x-axis now viewed as the polar axis and the origin as the pole. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane. In this section, we introduce to polar coordinates, which are points labeled ( r, θ )Īnd plotted on a polar grid. However, there are other ways of writing a coordinate pair and other types of grid systems. When we think about plotting points in the plane, we usually think of rectangular coordinates ( x, y ) How can the sailor indicate his location to the Coast Guard? In this section, we will investigate a method of representing location that is different from a standard coordinate grid. Over 12 kilometers from port, a sailboat encounters rough weather and is blown off course by a 16-knot wind (see ). Identify and graph polar equations by converting to rectangular equations.Transform equations between polar and rectangular forms.Convert from rectangular coordinates to polar coordinates.Convert from polar coordinates to rectangular coordinates.

Polar coordinates and polar graphs worksheet