Polar to cartesian conversion formulas, Mathematics

Assignment Help:

Polar to Cartesian Conversion Formulas

x = r cos Θ

y = r sin Θ

Converting from Cartesian is more or less easy.  Let's first notice the subsequent.

x2 + y2  = (r cosΘ)2 + (r sinΘ)2

= r2 cos2 Θ + r2 sin2 Θ

= r2 (cos2 Θ + sin2 Θ) = r2

This is a very helpful formula that we should keep in mind, though we are after an equation for r so let's take the square root of both sides. This provides,

r = √x2 + y2

Note: Technically we should have a plus or minus in front of the root as we know that r can be either positive or negative.  We will run along with the convention of positive r here.

Getting an equation for Θ is approximately as simple.  We'll begin with,

y/x = r sinΘ / r cos Θ = tan Θ

Taking the inverse tangent of both of the sides gives,

Θ = tan-1 (y/x)

We will require to be careful with this as inverse tangents only return values in the range - Π/2 < Θ < Π/2.  Remind that there is a second possible angle and that the second angle is provided by Θ + Π.

After that Summarizing gives the subsequent formulas for transforming from Cartesian coordinates to polar coordinates.

Cartesian to Polar Conversion Formulas

r2 = x2 + y2                                          

r = √ (x2 + y2)

Θ = tan -1 (y/x)


Related Discussions:- Polar to cartesian conversion formulas

Making connections with maths, MAKING CONNECTIONS :  you have read about w...

MAKING CONNECTIONS :  you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo

Estimate the last month sales increased through only 1/2%, Sales increased ...

Sales increased through only 1/2% last month. If the sales from the previous month were $152,850, what were last month's sales? Multiply through the decimal equivalent of 1/2 %

What is unitary method, Explanation of  Unitary Method Unitary Method k...

Explanation of  Unitary Method Unitary Method keeps of following two steps:-      Step 1 involves find the value of one unit.      Step 2 involves find the value of requi

Create a circular table with no restrictions, 1. Four different written dri...

1. Four different written driving tests are administered by a city. One of these tests is selected at random for each applicant for a drivers license. If a group of 2 women and 4 m

Find the height of the building, A building is in the form of a cylinder su...

A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains   41(19/21-) cu m of air. If the internal diameter of the building is equal to its t

Linear Equations, y= -3x tell if it is linear or not. our teacher wants it ...

y= -3x tell if it is linear or not. our teacher wants it graphed or something.

How long will it take the light to blink 405 times, The light on a lighthou...

The light on a lighthouse blinks 45 times a minute. How long will it take the light to blink 405 times? Divide 405 by 45 to get 9 minutes.

Hcf, the length of three pieces of ropes are 140cm,150cm and 200cm.what is ...

the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?

Find the sum of given equation upto n limit, Find the sum of (1 - 1/n ) + (...

Find the sum of (1 - 1/n ) + (1 - 2/n ) + (1 - 3/n ) ....... upto n terms. Ans: (1 - 1/n ) + (1 - 2/n ) - upto n terms   ⇒[1+1+.......+n terms] - [ 1/n + 2/n +....+

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd