Polar equations calculator - Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

 
A Polar Double Integral Calculator is an online calculator that can easily solve double definite integral for any complex polar equation. Double integration for polar point is the process of integration in which upper and lower limits for both dimensions are known. By applying double integration to the equation, we get a real definite value.. Craigslist asheville nc campers

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Area Between Polar Curves | Desmos. Function f is the green curve. f θ = 4 sin 2θ. Function g is the blue curve. g θ = 2. This is the Area between the two curves. n1 2 ∫α1 α0 f θ 2dθ + n2 2 ∫β1 β0 g θ 2dθ. Number of green sections needed to complete or negate in order to achieve desired area. n1 = 8.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 TrigonometryChanging 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 …Apr 28, 2018 ... How you can utilize your TI-Nspire Calculator in order to perform arithmetic as well as convert between rectangular and polar coordinates.Given that we're calculating for the second derivative of the polar coordinate system we have to use the equation d^2(y)/d^2(x) = (d/dt(dy/dx))/(dx/dt) $\endgroup$ - CaffeineDependent. ... How to check if derivative equation is correct? 1. How to find the second derivative of $2x^3 + y^3 = 5$? 1.Click on the menu from the top-left corner of the screen and select ' Graphing .'. You will then see a two-dimensional plotting surface where you can input equations and find out what their ...Here's a a quick video tutorial on polar graphing in the Desmos Graphing Calculator (https://www.desmos.com/calculator).You can find more how-to videos, as w...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 TrigonometryThe textbook is, "Differential Equations with Applications and Historical Notes, 3rd edition", by Simmons and Finlay. Can you please be more precise with regards to what's wrong with my/the textbooks calculations? I've only just begun studying differential equations so I really don't understand much. $\endgroup$ -The 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 [latex]\theta =\frac{\pi }{2}[/latex], the polar axis, or the pole.Photomath is a revolutionary mobile application that has taken the math world by storm. With just a simple snap of a photo, this app can solve complex mathematical equations in sec...Area in Polar Coordinates Calculator. Calculate the area of a polar function by inputting the polar function for "r" and selecting an interval. Get the free "Area in Polar Coordinates Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.This page explains how to plot a polar equation in Graphing Calculator 3D. Steps: Select "2D" from the graph dropdown list. Change the coordinates option from "Cartesian" to "Polar" in the dropdown list. Type in a polar equation using variables r and θ. To insert θ press Ctrl+1; Alternatively, click on KeyPad tab then click on θ button. ...θ r 2 = x 2 + y 2 tan. ⁡. θ = y x. This means that whenever we're given a polar equation, we can convert it to rectangular form by using any of the four equations shown above. Rewrite the polar equation so that it's in terms of r cos. ⁡. θ, r sin. ⁡. θ, and tan.2. powered by. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Get the free "ARC LENGTH OF POLAR FUNCTION CURVE" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Explore 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) | DesmosLet's take a look at a few problems that involve intersections of polar curves. 1. Solve the following system of equations algebraically: x 2 + 4 y 2 − 36 = 0 x 2 + y = 3. Before solving the system, graph the equations to determine the number of points of intersection. The graph of x 2 + 4 y 2 − 36 = 0 is an ellipse and the graph ...r = r (θ) is a continuous function. Illustrate approximating the area inside the graph of r from θ = a to θ = b by adding up the areas of ten appropriate circle sectors. You must shade the appropriate regions and calculate their combined area. r θ = 3 sin 2θ + 1. f x = 3 sin 2x + 1. a = 0. b = 3. 1 2 b − a 10 f 0b + 10a 10 2 + f b + 9a ...polar form. Have a question about using Wolfram|Alpha? Contact Pro Premium Expert Support ». Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….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 Trigonometrye. = eccentricity. Po. = orbital period. Vo. = orbital velocity. Rsyn. = Synchronous Orbit. The planetary calculator performs simultaneous calculations for all of the planets in the Solar System using current physical and orbital data.In today’s digital age, technology has revolutionized the way we learn and solve complex problems, particularly in the field of mathematics. Gone are the days when students relied ...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 TrigonometryTo 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.Free Ellipse calculator - Calculate ellipse area, center, radius, foci, vertice and eccentricity 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 ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. 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 2.7-08 Graphs of Polar Equations. Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid. John 14:27 NIV. 7-08 Graphs of Polar Equations. Mr. Wright teaches the lesson. Summary: In this section, you will: Graph polar equations.We enter values of θ θ into a polar equation and calculate r. r. However, using the properties of symmetry and finding key values of θ θ and r r means fewer calculations will be needed. Finding Zeros and Maxima. To find the zeros of a polar equation, we solve for the values of θ θ that result in r = 0. r = 0.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 TrigonometryEquations 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 TrigonometryWinter Storm Grayson is bringing snow and ice, followed by a frigid polar vortex. Here are 10 great clothing deals to keep you warm. By clicking "TRY IT", I agree to receive newsle...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.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 full version of this precalculus video tutorial focuses on graphing polar equations. It explains how to graph circles, limacons, cardiods, rose curves, ...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 TrigonometryTo 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 ...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 standard form of a quadratic equation is y = ax² + bx + c.You can use this vertex calculator to transform that equation into the vertex form, which allows you to find the important points of the parabola - its vertex and focus.. The parabola equation in its vertex form is y = a(x - h)² + k, where:. a — Same as the a coefficient in the standard form;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 TrigonometryA polar to rectangular equation calculator helps in converting a polar equation into its equivalent rectangular equation. Polar equations are expressed in terms of angles (θ) and distances (r) from the origin. The calculator allows you to input the polar equation and performs the conversion, providing the corresponding rectangular equation.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 \(r=2 \cos \left(\theta-90^{\circ}\right)\).The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = rcostheta (1) y = rsintheta, (2) where r is the radial distance from the origin, and theta is the counterclockwise angle from the x-axis. In terms of x and y, r = sqrt(x^2+y^2) (3) theta = tan^(-1)(y/x).The world's most advanced graphing calculator. Graph functions, equations (including implicit functions), parametric curves and points in the Cartesian and polar coordinate systems. Find x-intercepts, calculate symbolic derivatives and graph them. Additionally, ...Polar form. Settings: Find approximate solution Hide steps. Compute. example 1: Find the complex conjugate of z = 32 −3i. example 2: Find the modulus of z = 21 + 43i. example 3: Find the inverse of complex number 3−3i.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.I've been trying to create a polar equation that will give me all points on an ellipse with the independent variable being theta and the dependent variable being the radius, but I'm having a great deal of trouble wrapping my mind around how to accomplish such a feat.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. ... Use a graphing calculator to find the polar coordinates of [latex]\left(3,-4\right)[/latex] in degrees. Round to the nearest hundredth. 73 ...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 ...Graphing Polar Equations. 1. From the Graph Entry/Edit menu, select Polar. 2. Type an expression for rn ( θ ). 3. (Optional) Edit the default values for θmin, θmax, and θstep. 4. Press Enter.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...These problems work a little differently in polar coordinates. Here is a sketch of what the area that we'll be finding in this section looks like. We'll be looking for the shaded area in the sketch above. The formula for finding this area is, A = ∫β α1 2r2dθ. Notice that we use r in the integral instead of f(θ) so make sure and ...In today’s digital age, technology has revolutionized the way we learn and solve complex problems, particularly in the field of mathematics. Gone are the days when students relied ...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 Have a question about using Wolfram|Alpha? Contact Pro Premium Expert Support ». Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…. If a taxpayer is concerned that tax rates could go up in the future, converting to Roth takes tax rate changes out of the equation. Calculators Helpful Guides Compare Rates Lender ...2x-2y+z=-3 x+3y-2z=1 3x-y-z=2; This calculator solves Systems of Linear Equations with steps shown, using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule.Also you can compute a number of solutions in a system (analyse the compatibility) using Rouché-Capelli theorem.. Leave extra cells empty to enter non-square matrices.; You can use decimal fractions or mathematical ...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.Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...The full version of this precalculus video tutorial focuses on graphing polar equations. It explains how to graph circles, limacons, cardiods, rose curves, ...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! …Convert the rectangular coordinates (3, 3) to polar coordinates. Solution. We see that the original point (3, 3) is in the first quadrant. To find θ, use the formula tan θ = y x. This gives. tan θ tan θ tan−1(1) = 3 3 = 1 = π 4. To find r, we substitute the values for x and y into the formula r = x2 +y2− −−−−−√.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 ...Calculator's answer: (6.32∠71.6) Your answer: 6.32∠71.6° B. Find (2+j6)(3∠5°)/(2∠0.8 radians) in polar notation using degrees Solution: This tricky because one angle is in degrees, the other in radians. Convert the one in radians to rectangular first, then sub that in the rest of the equation.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 TrigonometryEquations 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 ... solve-for-equation-calculator. en. Related Symbolab blog posts. High ...cartesian to polar. Have a question about using Wolfram|Alpha? Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….In today’s digital age, calculators have become an essential tool for both professionals and students alike. Whether you’re working on complex mathematical equations or simply need...Graphing Polar Equations. 1. From the Graph Entry/Edit menu, select Polar. 2. Type an expression for rn ( θ ). 3. (Optional) Edit the default values for θmin, θmax, and θstep. 4. Press Enter.It can also convert complex numbers from Cartesian to polar form and vice versa. Example 1: Perform addition (2 + 3i) + (1 - 4i) leaving the result a) in polar form and b) in rectangular form. Example 2: Find a square root of 10 ∠ 35° leaving the result a) in polar form, b) in rectangular form. Cartesian Polar. degree radian. First number ...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.Graphing in Polar Coordinates. A typical polar equation is in the form r = f (θ), where f is some function ( of θ ). θ is the independent variable, and r is the dependent variable. The graph of a polar equation is the collection of all points that have at least one set of polar coordinates that satisfy the equation (remember that a point has ... 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. 1. Understand how polar equations work. Coordinates in polar equations are of the form (r,θ), where r represents radius and θ represents angle. This means you rotate θ radians around and go out r units. [2] 2. Make a table with values of the angle and radius. Take any random values of θ (around ten values would suffice) and calculate r ...The Graph Polar Equations Calculator is an online calculator that can be used to draw the polar graph of a polar equation, whereas plotting it manually is a difficult task. This online calculator is available in the browser, so you don't need to install or download any specific application. All this tool requires is simply the polar ...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 and the arbitrary point. Example: Convert (r, θ) = (2, 9) to Cartesian coordinates. Solution: To convert this the polar to rectangular calculator use the ...

A Polar Double Integral Calculator is an online calculator that can easily solve double definite integral for any complex polar equation. Double integration for polar point is the process of integration in which upper and lower limits for both dimensions are known. By applying double integration to the equation, we get a real definite value.. What is katie pavlich net worth

polar equations calculator

In the realm of scientific research, accurate calculations are essential for ensuring reliable results. Whether you are an astrophysicist working on complex equations or a chemist ...g θ = 1. a = 0.41. This is a tool for visualizing polar intersections. Change the functions for f and g and watch them be plotted as theta goes from 0 to 2π. If both graphs share the same ordered pair (r,θ), then, a they are plotted the two points will meet. If one graph crosses the other while the other graph is being plotted elsewhere ...While we're often familiar with functions that output just one variable and are graphed with Cartesian coordinates, there are other possibilities! Vector-valued functions, for example, can output multiple variables. Polar functions, too, differ, using polar coordinates for graphing. We can still explore these functions with derivatives and integrals.The procedure to use the rectangular to polar calculator is as follows: Step 1: Enter the x and y coordinate in the respective input field. Step 2: Now click the button “Calculate Polar Coordinates” to get the result. Step 3: Finally, the polar coordinates will be displayed in the output field.Business Contact: [email protected] Playlist: https://www.youtube.com/playlist?list=PL3Gnjw2fQSnE6P7bLxwz5PbGixT5dbrrBIn this tutorial, we go over how...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 TrigonometryWe 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 ...Matador is a travel and lifestyle brand redefining travel media with cutting edge adventure stories, photojournalism, and social commentary. DESPITE THEIR APPARENT monolithic still...Enter the equation for which you want to find all complex solutions. The Complex Number Calculator solves complex equations and gives real and imaginary solutions. Step 2: Click the blue arrow to submit. Choose "Find All Complex Number Solutions" from the topic selector and click to see the result in our Algebra Calculator ! ExamplesAs a result, Wolfram|Alpha also has separate algorithms to show algebraic operations step by step using classic techniques that are easy for humans to recognize and follow. This includes elimination, substitution, the quadratic formula, Cramer's rule and many more. Free Online Equation Calculator helps you to solve linear, quadratic and ...The drag polar is a fundamental aspect of aircraft design and performance analysis. ... The skin friction coefficient and wing to fuselage interference factor can be obtained using the links to the calculators provided. ... We introduce a number of additional terms in the equation below; namely a lifting surface correction factor, and a factor ...Get the free "Convert Complex Numbers to Polar Form" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.The polar function graphing calculator computes the signed distance r(θ) and locates that point along the radial axis. The polar function grapher then connects this point to the … Polar to Rectangular. Convert from polar form with magnitude and angle in degrees to rectangular (real and imaginary) in numerical form. Get the free "Polar to Rectangular" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. Polar to Rectangular. Convert from polar form with magnitude and angle in degrees to rectangular (real and imaginary) in numerical form. Get the free "Polar to Rectangular" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.The HP 50g is a powerful graphing calculator that has become a staple in the world of advanced mathematics. One of its standout features is the equation library, which allows users...When using polar coordinates, the equations \(\theta=\alpha\) and \(r=c\) form lines through the origin and circles centered at the origin, respectively, and combinations of these curves form sectors of circles. It is then somewhat natural to calculate the area of regions defined by polar functions by first approximating with …Rewrite the Cartesian Equation as a Polar Equation x^2+y^2=25. Step 1. Since , replace with . Step 2. Since , replace with . Step 3. Solve for . Tap for more steps... Step 3.1. Subtract from ... If any individual factor on the left side of the equation is equal to , the entire expression will be equal to . Step 3.5. Set equal to and solve for ...The general polar equation used with ellipses, parabolas, and hyperbolas does not apply to circles. Since e = 0 for circles, the equation would simplify to r = 0, which does not tell us much about the circle. Instead, the polar equation of a circle with radius r = a 2, or a equal to the diameter of the circle, passing through the origin, and having a center located at an angle β ....

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