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If the polar coordinates of a point P are (r,a) then
the rectangular coordinates of P are x = rcos(a) and y = rsin(a).
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Why you need more than one coordinate system?
That is because - for example - some calculations are easier in polar coordinates, and some are easier in rectangular coordinates. For example, complex numbers are easier to add and subtract in rectangular coordinates, and easier to multiply and divide in polar coordinates.
Method for the addition of vector?
Divide the vectors into horizontal and vertical components (or components in three dimensions). Add the components together for the different vectors. Convert the resultant vector back to polar coordinates, if need be. Note: Most scientific calculators have a special function to convert from polar coordinates (distance and angle) to rectangular coordinates (x and y coordinates), and back. If your calculator has such a function, using it will save you a lot of work.
How complex quantity can be expressed?
Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.
What are absolute relative and polar coordinates?
absolute relative and polar coordinates definition
Find the resultant of 150N and 200N acting at an angle of 30?
Here is how to solve this. Decide on a direction for each vector. Use your scientific calculator to do a polar-to-rectangular conversion - i.e., separate each vector in horizontal and vertical components. (Check your calculator's manual on how to carry out a polar-to-rectangular conversion.) Add the vectors by components. Finally, convert back to polar (rectangular-to-polar conversion, on your scientific calculator).
The following rectangular coordinates can be expressed by the polar coordinates: (4,pi)?
(-4,0)
How a vector can be expressed polar component?
I will assume a vector in a plane - in two dimensions. The idea of polar coordinates is that the vector is expressed as its length, and an angle. If you already have the vector in rectangular coordinates, i.e. the x and y components, most scientific calculators have a function that might be labelled R->P, to convert from rectangular coordinates to polar coordinates. Otherwise, use basic trigonometry - but using the specialized function is much faster, if your calculator has it.
The following rectangular coordinates can be expressed in the form of the polar coordinates: (6sqrt2,3pi/4)?
(-6,6)
How do you convert a complex number from polar form into rectangular form?
If the polar coordinates of a complex number are (r,a) where r is the distance from the origin and a the angle made with the x axis, then the cartesian coordinates of the point are: x = r*cos(a) and y = r*sin(a)
Why you need more than one coordinate system?
That is because - for example - some calculations are easier in polar coordinates, and some are easier in rectangular coordinates. For example, complex numbers are easier to add and subtract in rectangular coordinates, and easier to multiply and divide in polar coordinates.
What does POL function stand for in a scientific calculator?
The Pol function converts rectangular coordinates to polar coordinates
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)
Method for the addition of vector?
Divide the vectors into horizontal and vertical components (or components in three dimensions). Add the components together for the different vectors. Convert the resultant vector back to polar coordinates, if need be. Note: Most scientific calculators have a special function to convert from polar coordinates (distance and angle) to rectangular coordinates (x and y coordinates), and back. If your calculator has such a function, using it will save you a lot of work.
Convert the rectangular coordinates 5 and -12 to polar coordinates Round all answers to two decimal places?
r=sqrt(x2+y2) and θ=arctan(y/x) are useful formulae here. if x=5 and y=-12, r=13 and θ=arctan(-12/5)=-1.18 rectangular: (5,-12) ; polar: (13,-1.18)
450 neuton on a 10 degree angle and 380 neuton on a 30 degree angle. What are the resultant of two forces?
You can use a scientific calculator to convert from polar coordinates (length and direction) to rectangular coordinates (x-coordinate and y-coordinate). Most calculators have such a function directly; it is much easier to use this, than to use the special trigonometric formulae. Then, add the x- and y-components separate. You may want to convert the end-result back to polar coordinates - once again, use the special functions on your calculator, in this case, rectangular-to-polar conversion.
Do rectangular coordinates have the same property as polar coordinates?
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.
