| 单词 | polar coordinate |
| 例句 | Eventually she leads us toward more abstract concepts such as the polar coordinate system, a graphical approach to defining a point using distance and angle, as well as irrational numbers and decimals that repeat infinitely. Today’s Deep-Sea Explorers Are Mineral Miners and Ultrawealthy Hobbyists 2023-06-20T04:00:00Z The polar coordinate system provides an alternative way to locate points in the plane. Calculus, Volume 3 2016-03-30T00:00:00Z Using the definitions of the focal parameter and eccentricity of the conic section, we can derive an equation for any conic section in polar coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z In this section, we introduce to polar coordinates, which are points labeled and plotted on a polar grid. Algebra and Trigonometry 2015-02-13T00:00:00Z Instead of using stodgy Cartesian coordinates, Black Rock City is organized along polar coordinates, making its coordinate system unique among massive fire-themed desert art festivals. Burning Man's Mathematical Underbelly 2018-09-14T04:00:00Z Right, firing rate as a function of head direction during random foraging, plotted in polar coordinates. Mapping of a non-spatial dimension by the hippocampal–entorhinal circuit : Nature : Nature Research 2017-03-28T04:00:00Z This is exactly the same process that we followed in Introduction to Parametric Equations and Polar Coordinates to convert from polar coordinates to two-dimensional rectangular coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z The polar coordinate system provides an alternative method of mapping points to ordered pairs. Calculus, Vol 2 2016-03-30T00:00:00Z For the following exercises, convert the given polar coordinates to Cartesian coordinates. Algebra and Trigonometry 2015-02-13T00:00:00Z Critical mathematical applications such as Fourier transforms, Riemann zeta functions, Gaussian distributions, roots of unity, integrating over polar coordinates and pretty much anything involving trigonometry employs pi. Why Tau Trumps Pi 2014-06-25T04:00:00Z Right, firing rate as a function of head direction during random foraging, plotted in polar coordinates. Mapping of a non-spatial dimension by the hippocampal–entorhinal circuit : Nature : Nature Research 2017-03-28T04:00:00Z Grid lines for spherical coordinates are based on angle measures, like those for polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z In this section we see that in some circumstances, polar coordinates can be more useful than rectangular coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z Use a graphing calculator to find the polar coordinates of in degrees. Algebra and Trigonometry 2015-02-13T00:00:00Z The complex number 1+i, written in rectangular and polar coordinates. What Are Roots of Unity? 2013-02-07T21:15:00.597Z In the geometry of motion under central forces the advantage of working with polar coordinates is great. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Use the conversion formulas to convert equations between rectangular and polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z The polar coordinate system is well suited for describing curves of this type. Calculus, Vol 2 2016-03-30T00:00:00Z Use a graphing calculator to find the polar coordinates of in degrees. Algebra and Trigonometry 2015-02-13T00:00:00Z This method of specifying a point with a length and a direction is called using polar coordinates, and it shows up most beautifully in Euler’s identity, eiπ=-1. What Are Roots of Unity? 2013-02-07T21:15:00.597Z To apply a double integral to a situation with circular symmetry, it is often convenient to use a double integral in polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z This is a familiar problem; recall that in two dimensions, polar coordinates often provide a useful alternative system for describing the location of a point in the plane, particularly in cases involving circles. Calculus, Volume 3 2016-03-30T00:00:00Z However, if we use polar coordinates, the equation becomes much simpler. Calculus, Vol 2 2016-03-30T00:00:00Z This is one application of polar coordinates, represented as We interpret as the distance from the sun and as the planet’s angular bearing, or its direction from a fixed point on the sun. Algebra and Trigonometry 2015-02-13T00:00:00Z Use polar coordinates to find the volume inside the cone z = 2 − and above the xy-plane. Calculus, Volume 3 2016-03-30T00:00:00Z As with rectangular coordinates, we can also use polar coordinates to find areas of certain regions using a double integral. Calculus, Volume 3 2016-03-30T00:00:00Z 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. Calculus, Volume 3 2016-03-30T00:00:00Z We will use parametric equations and polar coordinates for describing many topics later in this text. Calculus, Vol 2 2016-03-30T00:00:00Z In this section, we will focus on the polar system and the graphs that are generated directly from polar coordinates. Algebra and Trigonometry 2015-02-13T00:00:00Z Earlier in this chapter we showed how to convert a double integral in rectangular coordinates into a double integral in polar coordinates in order to deal more conveniently with problems involving circular symmetry. Calculus, Volume 3 2016-03-30T00:00:00Z Figure 5.50 Cylindrical coordinates are similar to polar coordinates with a vertical z coordinate added. Calculus, Volume 3 2016-03-30T00:00:00Z Starting with polar coordinates, we can follow this same process to create a new three- dimensional coordinate system, called the cylindrical coordinate system. Calculus, Volume 3 2016-03-30T00:00:00Z In the polar coordinate system, each point also two values associated with it: r and θ. Calculus, Vol 2 2016-03-30T00:00:00Z To graph in the polar coordinate system we construct a table of and values. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, the integrals have been converted to polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z In the following exercises, convert the integrals to polar coordinates and evaluate them. Calculus, Volume 3 2016-03-30T00:00:00Z In this way, cylindrical coordinates provide a natural extension of polar coordinates to three dimensions. Calculus, Volume 3 2016-03-30T00:00:00Z Convert each of the following points into polar coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z Calculating direction follows the same straightforward process we used for polar coordinates. Algebra and Trigonometry 2015-02-13T00:00:00Z We can use polar coordinates in those planes if necessary. Calculus, Volume 3 2016-03-30T00:00:00Z We also used this idea when we transformed double integrals in rectangular coordinates to polar coordinates and transformed triple integrals in rectangular coordinates to cylindrical or spherical coordinates to make the computations simpler. Calculus, Volume 3 2016-03-30T00:00:00Z Figure 1.39 A partition of a typical curve in polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z Therefore this point can be represented as ⎛ 2, π ⎞ in polar coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z TRY IT #3 Write the polar coordinates as rectangular coordinates. Algebra and Trigonometry 2015-02-13T00:00:00Z As an example, we will use polar coordinates to find the volume of structures such as l’Hemisfèric. Calculus, Volume 3 2016-03-30T00:00:00Z Sometimes making the change to polar coordinates can also be very helpful. Calculus, Volume 3 2016-03-30T00:00:00Z In polar coordinates, the shape we work with is a polar rectangle, whose sides have constant r -values and/or constant θ -values. Calculus, Volume 3 2016-03-30T00:00:00Z Therefore this point can be represented as ⎛10, − π ⎞ in polar coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z How are polar coordinates different from rectangular coordinates? Algebra and Trigonometry 2015-02-13T00:00:00Z This is essentially the same thing as when we used polar coordinates in the xy -plane, except we are replacing y by z. Calculus, Volume 3 2016-03-30T00:00:00Z Give two sets of polar coordinates for each point. Calculus, Vol 2 2016-03-30T00:00:00Z Double integrals are sometimes much easier to evaluate if we change rectangular coordinates to polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z The polar coordinate system appears in the following figure. Calculus, Vol 2 2016-03-30T00:00:00Z For the following exercises, convert the given Cartesian coordinates to polar coordinates with Remember to consider the quadrant in which the given point is located. Algebra and Trigonometry 2015-02-13T00:00:00Z Figure 7.39 A partition of a typical curve in polar coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z Some formulas that produce the graph of a circle in polar coordinates are given by and See Example 3. Algebra and Trigonometry 2015-02-13T00:00:00Z Again, just as in Double Integrals over Rectangular Regions, the double integral over a polar rectangular region can be expressed as an iterated integral in polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z To plot a point in the polar coordinate system, start with the angle. Calculus, Vol 2 2016-03-30T00:00:00Z For the following exercises, find the polar coordinates of the point. Algebra and Trigonometry 2015-02-13T00:00:00Z Each of these orbits can be modeled by a conic section in the polar coordinate system. Algebra and Trigonometry 2015-02-13T00:00:00Z This is not the case when graphing in polar coordinates. Algebra and Trigonometry 2015-02-13T00:00:00Z Now that we have sketched a polar rectangular region, let us demonstrate how to evaluate a double integral over this region by using polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z The general idea behind graphing a function in polar coordinates is the same as graphing a function in rectangular coordinates. Calculus, Vol 2 2016-03-30T00:00:00Z Use a graphing calculator to find the polar coordinates of in radians. Algebra and Trigonometry 2015-02-13T00:00:00Z Convert to polar coordinates, and then plot the point. Algebra and Trigonometry 2015-02-13T00:00:00Z As a result, we tend to use polar coordinates to represent these orbits. Algebra and Trigonometry 2015-02-13T00:00:00Z Notice in the next example that integration is not always easy with polar coordinates. Calculus, Volume 3 2016-03-30T00:00:00Z This process generates a list of ordered pairs, which can be plotted in the polar coordinate system. Calculus, Vol 2 2016-03-30T00:00:00Z To convert from polar coordinates to rectangular coordinates, use the formulas and See Example 3 and Example 4. Algebra and Trigonometry 2015-02-13T00:00:00Z |
| 随便看 |
|
英语例句辞典收录了117811条英语例句在线翻译词条，基本涵盖了全部常用单词及词组的例句翻译及用法，是英语学习的有利工具。