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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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.
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.
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.
absolute relative and polar coordinates definition
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).