Confused About Manual Calculation of r & θ

In summary, the purpose of manually calculating r and θ is to determine the polar coordinates of a point in a two-dimensional coordinate system. This can be useful in various scientific and mathematical applications, such as in graphing and analyzing functions. To manually calculate r and θ, you will need the Cartesian coordinates (x, y) of the point and use specific formulas. While calculators can also be used to find polar coordinates, it is important to understand the manual calculation process for a better understanding. Polar coordinates are commonly used in physics, engineering, and mathematics for describing the position, velocity, and acceleration of objects moving in a circular or curved path. However, they do have limitations, such as not accurately representing points on the x-
  • #1
blackandyello
11
0
i tried evaluating this http://www4a.wolframalpha.com/Calculate/MSP/MSP47881a005158fa72fi31000026df4f1iaf7g05e7?MSPStoreType=image/gif&s=49&w=109&h=39

and the correct answer r = 1.1147 and theta = 75.9


however, i tried to do it manually and ended with this

http://www4a.wolframalpha.com/Calculate/MSP/MSP25561a0055g7ha78cb0g0000166dhfc7i3hc7dhe?MSPStoreType=image/gif&s=14&w=134&h=37

with different r and theta. any ideas?

tnx
 
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  • #2
It is impossible to read your attachments.
 

1. What is the purpose of manually calculating r and θ?

The purpose of manually calculating r and θ is to determine the polar coordinates of a point in a two-dimensional coordinate system. This can be useful in various scientific and mathematical applications, such as in graphing and analyzing functions.

2. How do I manually calculate r and θ?

To manually calculate r and θ, you will need the Cartesian coordinates (x, y) of the point and use the following formulas:
r = √(x2 + y2)
θ = tan-1(y/x)
Make sure to convert the angle θ to the appropriate units (radians or degrees) depending on the context of your problem.

3. Can I use a calculator to find r and θ?

Yes, most scientific calculators have functions for calculating polar coordinates. Simply enter the Cartesian coordinates and use the appropriate function (usually labeled as "r" or "θ"). However, it is still important to understand the manual calculation process for a better understanding of polar coordinates.

4. What are the applications of using polar coordinates?

Polar coordinates are commonly used in physics, engineering, and mathematics to describe the position, velocity, and acceleration of objects moving in a circular or curved path. They are also useful in solving problems in vector calculus and complex analysis.

5. Are there any limitations to using polar coordinates?

While polar coordinates are useful in certain applications, they do have some limitations. One major limitation is that they cannot accurately represent points on the coordinate plane that are located on the x- or y-axis. Additionally, some mathematical operations may be more complicated in polar coordinates compared to Cartesian coordinates.

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