Polar equations calculator - Learn how to graph polar equations on the TI-84 graphing calculator and determine the polar coordinates of points on those graphs. Click Create Assignment to assign this modality to your LMS. We have a new and improved read on this topic.

 
Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry. Family dollar in smyrna

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry Polar Coordinates | Desmos. Loading... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Changing the mode on your TI-84. You can’t begin graphing polar equations until you change the mode of your calculator. Follow these steps to change the mode of your calculator: Press [MODE] and put the calculator in Polar mode. To highlight an item in the Mode menu, use the arrow keys to place the cursor on the item, and then …Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryExample 10.3.1: Plotting a Point on the Polar Grid. Plot the point (3, π 2) on the polar grid. Solution. The angle π 2 is found by sweeping in a counterclockwise direction 90° from the polar axis. The point is located at a length of 3 units from the pole in the π 2 direction, as shown in Figure 10.3.3. Figure 10.3.3.Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Polar Coordinates: Graphing Calculator. Save Copy. Log InorSign Up. r = sin 2 2. 4 · θ + cos 2. 4 · θ 4. 1. sin 2 2. 4 · t + cos 2. 4 · t 4 · cost, sin 2 2. 4 ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. The area of a region in polar coordinates defined by the equation \(r=f(θ)\) with \(α≤θ≤β\) is given by the integral \(A=\dfrac{1}{2}\int ^β_α[f(θ)]^2dθ\). To find the area between two curves in the polar coordinate system, first find the points of intersection, then subtract the corresponding areas.What 6 concepts are covered in the Polar Conics Calculator? angle. the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. conic. directrix. line in a parabola not through the focus. eccentricity. Deviation of a conic from a circular shape. polar conics.POLAR CAPITAL EMERGING MARKET STARS FUND INSTITUTIONAL SHARES- Performance charts including intraday, historical charts and prices and keydata. Indices Commodities Currencies Stock...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.To enable polar graphing, make sure the "POL" or "POLAR" option is selected. Polar graphing behaves differently depending on whether you are in radian or degree mode—usually, you'll want to work in radians. Mode menu on the TI-84+. "POL" is selected to enable polar graphing. Next, we can go to the equation entry screen by ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Rectangular-to-Polar grapher Ex. 2 | DesmosEquations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryArea of a Polar Region Let r be continuous and non-negative on [α, β], where 0 ≤ β − α ≤ 2π. The area A of the region bounded by the curve r(θ) and the lines θ = α and θ = β is. A = 1 2 ∫β α r(θ)2dθ. The theorem states that 0 ≤ β − α ≤ 2π. This ensures that region does not overlap itself, giving a result that does ... Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryOmni Calculator solves 3650 problems anywhere from finance and business to health. It's so fast and easy you won't want to do the math again! Your life in 3650 free calculators. Biology. 100 calculators. Chemistry. 100 calculators. Construction. 144 calculators. Conversion. 295 calculators. Ecology. 30 calculators. Everyday life.Take two Cartesian coordinates, x x, and y y. To calculate the polar coordinates corresponding to that pair, we need to use a bit of trigonometry, but don't worry: it's basic one. First, let's calculate the polar coordinates' radius: \footnotesize r = \sqrt {x^2+y^2} r = x2 + y2.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.The line segment starting from the center of the graph going to the right (called the positive x-axis in the Cartesian system) is the polar axis.The center point is the pole, or origin, of the coordinate system, and corresponds to r = 0. r = 0. The innermost circle shown in Figure 7.28 contains all points a distance of 1 unit from the pole, and is represented by the equation r = 1. r = 1.The Polar to Cartesian Coordinate Converter is an online tool that converts polar coordinates to Cartesian coordinates and vice versa. Cartesian coordinates, also known as rectangular coordinates, are a two-dimensional coordinate system formed by two perpendicular axes, usually labeled the x-axis and y-axis. The point where the two axes …To write a rectangular equation in polar form, the conversion equations of x = r cos θ x = r cos. ⁡. θ and y = r sin θ y = r sin. ⁡. θ are used. If the graph of the polar equation is the same as the graph of the rectangular equation, then the conversion has been determined correctly. Figure 5.2.3.1 5.2.3. 1. (x − 2)2 +y2 = 4 ( x − 2 ...To convert an equation given in polar form (in the variables #r# and #theta#) into rectangular form (in #x# and #y#) you use the transformation relationships between the two sets of coordinates: #x=r*cos(theta)# #y=r*sin(theta)# You have to remember that your equation may need some algebraic/trigonometric manipulations before being transformed into rectangular form; for example, consider:Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. ... Parametric Equations and Polar Coordinates. Convert to Polar. Step 1. Convert from rectangular coordinates to polar coordinates using the conversion formulas. Step 2.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Equation of a Line Gradient of a Line Polar Curves Parametric Curves Derivative Calculator Integral Calculator Formulas and Notes Equation Calculator Algebra Calculator. Graphing Calculator Plot Functions, Intercepts, Inverse. Enter the function. Use x as your variable. See Examples. y = log$_{ }{ }$ sin-1: cos-1:How to Use Polar to Rectangular Calculator? Please follow the below steps to convert polar to rectangular coordinates: Step 1: Enter the polar coordinates(r, θ) in the given input boxes. Step 2: Click on the "Convert" button to convert polar to rectangular coordinates. Step 3: Click on the "Reset" button to clear the fields and enter the different values.Free online graphing calculator - graph functions, conics, and inequalities interactivelyThe calculator is now set to graph polar equations. (Be sure your calculator is also in "Radian" MODE ). We can now graph the two equations for examples #1 and #2 in the lesson link to "Identifying and Graphing Polar Lines and Circles" as polar equations. Example #1: Graph the polar equations: 5 2sin cos r θ θ = +: (From Example #1) andHow to set up the mode and window and use the table to plot points of Polar Graph using a graphing calculatorTo find the full list of all Precalculus and Geo...Polar equations can be graphed by simply using r and theta instead of x and y. Type in "theta," and desmos will use the symbol for it. To graph on the polar grid, use the tool-shaped button in the ...We are used to working with functions whose output is a single variable, and whose graph is defined with Cartesian, i.e., (x,y) coordinates. But there can be other functions! For example, vector-valued functions can have two variables or more as outputs! Polar functions are graphed using polar coordinates, i.e., they take an angle as an input and output a radius! Learn about these functions ...It seamlessly translates polar coordinates (r, θ) into their rectangular counterparts (x, y). The conversion formulae at the core of this calculator are: x = r * cos(θ) y = r * sin(θ) Where: x is the rectangular x-coordinate. y is the rectangular y-coordinate. r is the polar radius (distance from the origin).Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryPolar Area Calculator. Equation to graph: (In terms of θ) r =. ≤ θ ≤. Step size:A great way to discover new types of graphs in polar coordinates is to experiment on your own with your calculator. Try to come up with equations and graphs that look similar to the following two polar functions. The circle in blue has a center at \(90^{\circ}\) and has a diameter of 2 . Its equation is \(r=2 \cos \left(\theta-90^{\circ}\right)\).Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry ... matrix-equation-calculator. en. Related Symbolab blog posts. Middle School Math ...A polar equation is any equation that describes a relation between \(r\) and \(\theta\), where \(r\) represents the distance from the pole (origin) to a point on a curve, and \(\theta\) represents the counterclockwise angle made by a point on a curve, the pole, and the positive \(x\)-axis.. Cartesian equations can be converted to polar equations using the …Similarly, converting an equation from polar to rectangular form and vice versa can help you express a curve more simply. Follow these five steps to convert equations between the polar and rectangular systems: Step 1: Identify the form of your equation. A quick glance at your equation should tell you what form it is in.To do it, simply polar coordinate calculator use the following polar equation to rectangular: $$ x = r * cos θ y = r * sin θ $$ The value y/x is the slope of the line that joining the pole …Polar Equation Slope Calculator. Added Mar 5, 2014 by Sravan75 in Mathematics. Inputs the polar equation and specific theta value. Outputs the tangent line equation, slope, and graph. Send feedback | Visit Wolfram|Alpha. Get the free "Polar Equation Slope Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle.This brief video demonstrates how to use the Casio fx-9750GIII calculator for plotting polar functions. It includes a few Zoom commands and Window commands a...Free Parabola calculator - Calculate parabola foci, vertices, axis and directrix step-by-step We've updated our ... Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry ...Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryExplore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Lesson 82 - Conversion of equations ( polar and rectangular) | DesmosExample 01: Draw the polar graph of the curve r=sin (θ). The first step is to make a table of values for r=sin (θ). We then plot each point on the coordinate axis. For example, to graph the point (r,θ), we draw a line with length equal to r from the point (0,0) and slope angle equal to θ. The endpoint of the line is the point (r,θ).You can find many links on the internet if you search the keyword online polar equation solver. Most of the information is however crafted for the readers who already have some knowledge about this subject. If you are a complete novice, you should use Algebrator. Is it easy to understand and very helpful too. Back to top.I love pickles and pickled things, but the cucumber pickle will forever be my favorite. Pickles are polarizing. Even people who like vinegar and cucumbers sometimes struggle to eat...Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryRectangular to Polar Coordinates – Formula. The Rectangular to Polar Coordinates – Formula is a helpful tool for calculating polar from rectangular coordinates and other equations. You can use this formula in science, engineering, and mathematics: r=\sqrt{x^{2}+y^{2}} Radius r is the distance from the origin, and θ is the angle from the x ...Polar to Rectangular Online Calculator. Below is an interactive calculator that allows you to easily convert complex numbers in polar form to rectangular form, and vice-versa. There's also a graph which shows you the meaning of what you've found. For background information on what's going on, and more explanation, see the previous pages,Take two Cartesian coordinates, x x, and y y. To calculate the polar coordinates corresponding to that pair, we need to use a bit of trigonometry, but don't worry: it's basic one. First, let's calculate the polar coordinates' radius: \footnotesize r = \sqrt {x^2+y^2} r = x2 + y2.2 Standard graphs in polar coordinates include circles and roses, cardioids and limaçons, lemniscates, and spirals. 3 To find the intersection points of the polar graphs r = f(θ) and r = g(θ) we solve the equation f(θ) = g(θ). In addition, we should always check whether the pole is a point on both graphs.Feb 1, 2023 ... Share your videos with friends, family, and the world.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.The Cartesian to Polar Coordinate Calculator serves as a tool to effortlessly convert Cartesian coordinates (x, y) into polar coordinates (r, θ). This conversion is crucial in various mathematical and scientific fields, aiding in visualizing positions, determining distances, and plotting vectors or complex equations on polar grids.Equation of a Line Gradient of a Line Polar Curves Parametric Curves Derivative Calculator Integral Calculator Formulas and Notes Equation Calculator Algebra Calculator. Graphing Calculator Plot Functions, Intercepts, Inverse. Enter the function. Use x as your variable. See Examples. y = log$_{ }{ }$ sin-1: cos-1:Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...A polar equation describes a curve on the polar grid. The graph of a polar equation can be evaluated for three types of symmetry, as shown in Figure 6.2.2. Figure 6.2.2: (a) A graph is symmetric with respect to the line θ = π 2 (y-axis) if replacing (r, θ) with ( − r, − θ) yields an equivalent equation.Example 1: Consider a solid cylindrical shaft with a radius 'r' of 5 cm subjected to a torque 'T'. Using our Polar Moment of Inertia Calculator, the inertia 'J' can be found, which is essential for predicting the shaft's ability to resist twisting. Example 2: For a hollow cylindrical pipe with an outer radius 'R' of 10 cm and an inner radius 'r ...Matrix Inverse Calculator; What are systems of equations? A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.Polar forms of numbers can be converted into their rectangular equivalents by the formula, Rectangular form= amplitude * cos (phase) + j (amplitude) * sin (phase). This is all based off the fact that the polar form takes on the format, amplitude < phase. So, for example, let's take the expression in polar form, 12 < 55°.To do it, simply polar coordinate calculator use the following polar equation to rectangular: $$ x = r * cos θ y = r * sin θ $$ The value y/x is the slope of the line that joining the pole …Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorldThe Polar to Cartesian Coordinate Converter is an online tool that converts polar coordinates to Cartesian coordinates and vice versa. Cartesian coordinates, also known as rectangular coordinates, are a two-dimensional coordinate system formed by two perpendicular axes, usually labeled the x-axis and y-axis. The point where the two axes meet is ...The conversion is. r = 2secθ r = 2 cosθ rcosθ = 2 x = 2. Notice that the equation r = 2secθ drawn on the polar grid is clearly the same as the vertical line x = 2 drawn on the rectangular grid (see Figure 6.3.14 ). Just as x = c is the standard form for a vertical line in rectangular form, r = csecθ is the standard form for a vertical line ...0. A way to think about this is is that you want to shift all θ θ to θ′ = θ + δ θ ′ = θ + δ, where δ δ is the amount by which you want to rotate. This question has a significance if you want to rotate some equation which is a function of theta. In the case r = θ r = θ that becomes r = θ + δ r = θ + δ. Of course if our ...The previous section discussed a special class of parametric functions called polar functions. ... Recall that Consequently, and therefore When , Thus the equation of the line (in polar rectangular coordinates) tangent to the limaçon at is . Consider the limaçon given by on the interval . Find Cartesian coordinates for the points where the ...The circle is centered at \((1,0)\) and has radius 1. The upcoming gallery of polar curves gives the equations of some circles in polar form; circles with arbitrary centers have a complicated polar equation that we do not consider here. Figure \(\PageIndex{10}\): Graphing \(xy=1\) from Example 9.4.6The equation has failed the symmetry test, but that does not mean that it is not symmetric with respect to the pole.Passing one or more of the symmetry tests verifies that symmetry will be exhibited in a graph. However, failing the symmetry tests does not necessarily indicate that a graph will not be symmetric about the line θ = π 2, θ = π 2, the polar axis, or the pole.The Formula Behind the Calculator. The area between two polar curves is found by integrating the difference of the squared functions representing the curves, with respect to the angle, over the given interval. The formula is as follows: A = 1/2 ∫ from α to β [ (f (θ))^2 - (g (θ))^2] dθ. Here, f (θ) and g (θ) are the functions ...Polar Equation Slope Calculator. Added Mar 5, 2014 by Sravan75 in Mathematics. Inputs the polar equation and specific theta value. Outputs the tangent line equation, slope, and graph. Send feedback | Visit Wolfram|Alpha. Get the free "Polar Equation Slope Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Two options for finding the distance between polar points. To find the distance between two polar coordinates, we have two options. We can either convert the polar points to rectangular points, then use a simpler distance formula, or we can skip the conversion to rectangular coordinates, but use a more complicated distance formula.If you are given the center and radius of the circle, follow these steps: Look at the general equation of a circle: (x − A)² + (y − B)² = r². Let A determine the x-coordinate of the center and B determine the y-coordinate. Determine the radius of the circle and substitute this value in place of r.This brief video demonstrates how to use the Casio fx-9750GIII calculator for plotting polar functions. It includes a few Zoom commands and Window commands a...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.To convert from the rectangular to the polar form, we use the following rectangular coordinates to polar coordinates formulas: r = √(x² + y²) θ = arctan(y / x) Where: x and y — Rectangular coordinates; r — Radius of the polar coordinate; and. θ — Angle of the polar coordinate, usually in radians or degrees. With these results, we ...polar equation describes a relationship between rr and θ on a polar grid. It is easier to graph polar equations if we can test the equations for symmetry. ... Using a graphing calculator, we can see that the equation \(r=2 \sin \theta\) is a circle centered at \((0,1)\) with radius \(r=1\) and is indeed symmetric to the line \(\theta=\dfrac ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.To convert polar equations to rectangular equations, we’ll use the conversion formulas x=rcos(theta), y=rsin(theta), and r^2=x^2+y^2. ... learn online, online course, online math, calculus 3, calculus iii, calc 3, calc iii, vector calculus, limit of a vector function, vector function limit . Online math courses. Get started Courses. Pre ...

Cartesian and Polar Grapher. To sketch the graph of a polar equation a good first step is to sketch the graph in the Cartesian coordinate system. This will give a way to visualize how r changes with θ. The information about how r changes with θ can then be used to sketch the graph of the equation in the polar coordinate system.. Kollel ncsy

polar equations calculator

Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry Given an equation in polar form, graph it using a graphing calculator. Change the MODE to POL , representing polar form. Press the Y= button to bring up a screen allowing the input of six equations: r 1 , r 2 , . . . , r 6 . r 1 , r 2 , . . . , r 6 . In today’s digital age, calculators have become an essential tool for both professionals and students. Whether you’re working on complex equations or simply need to calculate basic...Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryExplore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Free Circle equation calculator - Calculate circle's equation using center, radius and diameter step-by-step ... Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane ...Step 5: Connect the Points. Once you've plotted all your points, connect them with a smooth curve to complete the graph. It's a good idea to plot enough points to make sure your graph is accurate. Let's illustrate this process using the polar equation \ (r = cos (θ)\). Create a Table of Values.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Polar Graphing: Limacons/Cardioids | DesmosEquations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections TrigonometryFormulas for the Equation of a Circle. Some of the formulas that produce the graph of a circle in polar coordinates are given by r = acos θ and r = asin θ, where a is the diameter of the circle or the distance from the pole to the farthest point on the circumference. The radius is | a | 2, or one-half the diameter.Free derivative calculator - differentiate functions with all the steps. Type in any function derivative to get the solution, steps and graph ... Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. polar equation grapher. Save Copy. Log InorSign Up. t heta = 0. 1. f θ = 6 + a · sin bθ. 2. sweeper arm . 3. curve and point ...The relationship between polar and Cartesian coordinates is given by the formulas: x = r * cos (θ) and y = r * sin (θ). Polar coordinates (r, θ) represent a point’s distance and angle from the origin, while Cartesian coordinates (x, y) represent the point’s location on the XY-plane..

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