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- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/10%3A_Further_Applications_of_Trigonometry/10.03%3A_Polar_CoordinatesWhen we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and ...When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and other types of grid systems. In this section, we introduce to polar coordinates, which are points labeled (r,θ) and plotted on a polar grid. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/02%3A_Multiple_Integration/2.05%3A_Cylindrical_and_Spherical_CoordinatesIn this section, we look at two different ways of describing the location of points in space, both of them based on extensions of polar coordinates. As the name suggests, cylindrical coordinates are u...In this section, we look at two different ways of describing the location of points in space, both of them based on extensions of polar coordinates. As the name suggests, cylindrical coordinates are useful for dealing with problems involving cylinders, such as calculating the volume of a round water tank or the amount of oil flowing through a pipe. Similarly, spherical coordinates are useful for dealing with problems involving spheres, such as finding the volume of domed structures.
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/06%3A_The_Polar_System/6.01%3A_Polar_CoordinatesThe 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. To plot a point in the form (r,θ), θ>0, move in a co...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. To plot a point in the form (r,θ), θ>0, move in a counterclockwise direction from the polar axis by an angle of θ, and then extend a directed line segment from the pole the length of r in the direction of θ.
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/06%3A_The_Polar_System/6.03%3A_Converting_Between_Systems\[\begin{aligned} r &=\sin(2\theta) && \text{Use the double angle identity for sine.} \\[4pt] r &=2 \sin \theta \cos \theta && \text{Use }\cos \theta=\dfrac{x}{r} \text{ and } \sin \theta =\dfrac{y}{r...r=sin(2θ)Use the double angle identity for sine.r=2sinθcosθUse cosθ=xr and sinθ=yr.r=2(xr)(yr) Simplify.r=2xyr2Multiply both sides by r2.r3=2xy(x2+y2)3=2xyAs x2+y2=r2,r=√x2+y2.
- https://math.libretexts.org/Courses/Reedley_College/Trigonometry/04%3A_Further_Applications_of_Trigonometry/4.03%3A_Polar_CoordinatesWhen we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and ...When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and other types of grid systems. In this section, we introduce to polar coordinates, which are points labeled (r,θ) and plotted on a polar grid. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane.
- https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.04%3A_Polar_CoordinatesWhen we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and ...When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and other types of grid systems. In this section, we introduce to polar coordinates, which are points labeled (r,θ) and plotted on a polar grid. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/11%3A_Appendix_-_Prerequisite_Function_Material/11.01%3A_Sets_of_Real_Numbers_and_the_Cartesian_Coordinate_PlaneThis section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and...This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_(Lecture_Notes)/01%3A_Functions/1.02%3A_Domain_and_RangeFinding the Domain of a Function Defined by an Equation Examples Domain and range of a set of data points. Domain of a quadratic, simple rational, and shifted square root function. Note You will likel...Finding the Domain of a Function Defined by an Equation Examples Domain and range of a set of data points. Domain of a quadratic, simple rational, and shifted square root function. Note You will likely have to review interval notation. Definitions Set-builder notation Finding Domain and Range from Graphs Do one. Finding Domains and Ranges of the Toolkit Functions Graphing Piecewise-Defined Functions Definition Piecewise function Example Graph a piecewise involving raw toolkit functions only.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.01%3A_Sets_of_Real_Numbers_and_the_Cartesian_Coordinate_PlaneThis section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and...This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.03%3A_Polar_CoordinatesWhen we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and ...When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and other types of grid systems. In this section, we introduce to polar coordinates, which are points labeled (r,θ) and plotted on a polar grid. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane.
