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Do rectangular coordinates have the same property as polar coordinates?
Wiki User
∙ 10y ago
Some of them but not all.
For example, uniqueness.
The rectangular coordinates (x, y) represent a different point if either x or y is changed. This is also true for polar coordinate (r, a) but only if r > 0. For r = 0 the coordinates represent the same point, whatever a is. Thus (x, y) has a 1-to-1 mapping onto the plane but the polar coordinates don't.
Wiki User
∙ 10y ago
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In mathematical terms what is a box?
A rectangular prism. If every edge is the same length, then it is a cube.
What is the limit of sin3x times sin5x divided by x squared as x approaches 0?
For ease of writing, every time I say lim I mean the limit of _____ as x approaches zero. Lim sin3xsin5x/x^2=lim{[3sin(3x)/(3x)][5sin(5x)/(5x)]}. One property of limits is that lim sin(something)/(that same something)=1. So we now have lim{[3(1)][5(1)]}=15. lim=15
What is the french word for triangle?
It is the same word, same spelling but pronounced like -tree-on-glaHope this helps.
Different kinds of triangles in terms of sides?
An isosceles triangle has two sides the same length. An equilateral has all 3 sides the same length. A scalene triangle doesn't have any sides that are the same length.
What does truse mean?
A truse is an agreement to give up at the same time. The incorrect spelling of truce - which is an agreement to give up at the same time.
Which set of polar coordinates describes the same location as the rectangular coordinates (1,-1)?
(sqrt2, 315)
Which set of rectangular coordinates describes the same location as the polar coordinates (3sqrt2,5pi/4)?
(-3,-3)
which set of polar coordinates describes the same location as the rectangular coordinates (-5,0)?
(5, pi) or in other words, (5, 180)
Which set of polar coordinates describes the same location as the rectangular coordinates (0,-2) A. (-2,270) B. (2,0) C. (2,180) D. (-2,90)?
(-2, 90) apex, but another "expert verified answer" from brainly suggests (2,0)
How do you use polar coordinates in graphing?
In much the same way as you use rectangular coordinates.With Cartesian or rectangular coordinates, you start from the origin and move a distance of x in the horizontal direction and then a distance of y in the vertical direction.Using polar coordinates, you start from the origin along a ray inclined at an angle theta with the positive horizontal axis (clockwise from Eastwards), and you go a distance r along that ray.In all but degenerate cases the Cartesian coordinates of (r, theta) arex = r*cos(theta) and y = r*sin(theta)while, conversely,r = sqrt(x2 + y2) and theta = arctan(y/x).
What are the polar coordinates?
What are polar coordinates of (√2, 1)? Solution: Here we need to convert from rectangular coordinates to polar coordinates: P = (x, y) = (r, θ) r = ± √(x^2 + y^2); tan θ = y/x or θ = arc tan (y/x) So we have: P = (√2, 1) r = ± √[(√2)^2 + 1^2] = ± √3 θ = arc tan (y/x) = arc tan (1/√2) = arc tan (√2/2) ≈ 35.3°, which is one possible value of the angle. (√2, 1) is in the Quadrant I. If θ = 35.3°, then the point is in the terminal ray, and so r = √3. Therefore polar coordinates are (√3, 35.3°). Another possible pair of polar coordinates of the same point is (-√3, 215.3°) (180° + 35.3° = 215.3°). Edit: Note the negative in the r value.
What is the magnitude and direction of the resultant force of this situation Both angles have 30N force vector one is at 34 degrees and vector two is at 76 degrees 22 degrees between the two?
To add two vectors, you add the components. The angles are specified in polar coordinates (magnitude and angle); use the same convention for both angles (for example, measure them from the x-axis counterclockwise), then use your scientific calculator to convert from polar coordinates to rectangular coordinates. Most scientific calculators have a P->R conversion. After that, you can add the components of the vectors separately. Since you want the magnitude and direction of the resultant force, you then need to convert back to polar coordinates (R->P conversion, on your calculator).
How can you add vector quantities?
You can add vectors graphically (head-to-foot). Mathematically, you can add the individual components. For example, in two dimensions, separate the vector into x and y components, and add the x-component for both vectors; the same for the y-component.Here it may be useful to note that scientific calculator have a special function to convert from polar to rectangular coordinates, and vice-versa. If you RTFM (the calculator manual, in this case), it may help a lot - a vector may be given in polar coordinates (a length and an angle); using this special function on the calculator can do the conversion to rectangular (x- and y-components) really fast.
What is the answer to the question three parallel impedances Z1 Z2 and Z3 are represented by the complex numbers Z1 equals 2 plus j Z2 equals 1 plus j and Z3 equals j squared answer in polar cartesian?
The general rule for resistances in parallel (to find out the equivalent resistance) is: 1/R = 1/R1 + 1/R2 + 1/R3 + ... The same rule can be used for impedances (just replace resistance by impedance). So, you just have to divide 1 by each of the impedances, add the results together, then take the reciprocal. Note that addition and subtraction with complex numbers is easier if the numbers are in rectangular coordinates, whereas multiplication and division is easier if they are in polar coordinates. Also note that most scientific calculators have the capacity to convert between polar and rectangular coordinates. Check your calculator manual for details.
What are the imaginary cube roots of -125?
This can be done easily if you use polar coordinates. I did all of the following calculations in my head, without resorting to a calculator: One of the cubic roots of -125 is -5. That is the same as 5, at an angle of 180 degrees. The other two cubic roots also have an absolute value of 5, and each cubic root has an angle of 120 degrees to the other cubic roots. In other words, the complex roots are 5 at an angle of 60 degrees, and 5 at an angle of -60 degrees. If you want to convert this to rectangular coordinates (i.e., show the real and the imaginary parts separately), use the P-->R (polar to rectangular) conversion, available on most scientific calculators.
Why can't we add and subtract polar form of complex numbers and multiply and divide the rectangular form of complex number?
You can certainly multiply and divide with the rectangular form, but it is somewhat easier in polar form. This is especially relevant if you want to extend to more complicated operations, such as higher powers or taking roots. As for the polar form, any method to add and subtract them directly would probably be quite complicated, and directly or indirectly involve many of the same calculations that are done in converting from polar to rectangular, and back. Try it! (That is, try to deduce the formulas for adding two complex numbers in polar form.)
When does cos X equal sin X?
When the angle X = 45 or 225 degrees, or any other angle that falls at the same position as one of these angles in polar coordinates.
