1/19/2024 0 Comments Rectangular coordinates calculatorSo I'm going to constructĪ unit circle here. Use some trig functions to relate r, theta, and This a little bit, and to help us let's remind ourselves of the unit circleĭefinition of trig functions because we are going to Number in rectangular form, can you figure out what r and theta are? Well let's think through If you can find a relationship between r theta and Now what I want you to do right now is pause this video and see So if someone gave you thisĪngle and this distance, then you could get to z. Theta, in radians, this angle between the positive real axis and this line right over here, this line or the segment thatĬonnects the origin and z. and so to specify the direction, we will have this angle, You have to say in whatĭirection do you have to go a distance of r to get to z. So for example we could give the distance from the origin to z, so let's call this distance r, but that distance by itself Real and imaginary parts, essentially the coordinates here, let's think about giving a direction and a distance to get to z. Now what I want to thinkĪbout are other ways to essentially specify the location of z. So z is real part negative three, imaginary part two. Part is negative three, so we could go one, two, three So, this is our imaginary axisĪnd that is our real axis. So first let's think about where this is on the complex plane. Let's say that I have the complex number z and in rectangular form we can write it as negative three plus two i. Some calculators might do the job for you. Which allows us to conclude that arctan(-1) = -π/4. We can say that α = arctan(tan(α)) but how do we find the exact value of arctan(-1)? We know that an angle of π/4 has a tangent of 1. For example, let's say that we have 3 - 3i and want to know the angle (α) of this complex number. We can use those values to help us get the exact answer to a problem. With tan, you can remember that that tan(α) = sin(α)/cos(α). One easy way to remember them is that, in the sin row, the number given to sqrt gets incremented with each column, and that on the cos row it decrements with every column. However, by using the drop-down menu, the option can changed to radians, so that theĮxample With Rectangular (Cartesian) CoordinatesĬonvert the rectangular coordinates (2, 3, 8) into its equivalent spherical coordinates.These numbers and angles should be remembered. If desired toĬonvert a 3D rectangular coordinate, then the user enters values into all 3 form fields, X, Y, and Z.īy default, the calculator will compute the result in degrees. To convert a 2D rectangular coordinate, then the user just enters values into the X and Y form fields and leaves the 3rd field, the Z field, blank. This calculator can be used to convert 2-dimensional (2D) or 3-dimensional rectangular coordinates to its equivalent spherical coordinates. To use this calculator, a user just enters in the (X, Y, Z) values of the rectangular coordinates and then clicks the 'Calculate' button,Ĭoordinates will be automatically computed and shown below. When converted into spherical coordinates, the new values will be depicted as Rectangular coordinates are depicted by 3 values, (X, Y, Z). This spherical coordinates converter/calculator converts the rectangular (or cartesian) coordinates of a unit to its equivalent value in sphericalĬoordinates, according to the formulas shown above.
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