Need help with Trig/angle question

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SUMMARY

The discussion focuses on converting Cartesian coordinates to polar coordinates, specifically for the point (1, -1) in the fourth quadrant. The conversion formulas are established as r = √(x² + y²) and θ = arctan(y/x), with a reminder to adjust for the quadrant. Additionally, the conversation addresses the challenge of converting irrational angles, such as tan⁻¹(4/3) ≈ 53.1 degrees, into the format aπ + 2nπ, noting that such angles may not yield a rational representation.

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  • Understanding of Cartesian and polar coordinate systems
  • Familiarity with trigonometric functions, specifically arctangent
  • Knowledge of quadrant-specific angle adjustments
  • Basic algebra for manipulating square roots and irrational numbers
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  • Explore the implications of irrational numbers in trigonometric calculations
  • Investigate the use of radians versus degrees in mathematical contexts
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Students studying trigonometry, mathematics educators, and anyone needing to understand the conversion between Cartesian and polar coordinates.

jkh4
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For example: if i have a point (1, -1) in the forth quadrant of the xy plane. How do you convert it to angle = [7(pie)/2]+2n(pie) format? i just forget how to do that part. Also, what if the answer for tan-1(angle) is not a whole #, ex: 53.1, then how do you do the conversion? Thank you.
 
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To convert from rectangular (x,y) to polar (r,theta):
r=Sqrt[x^2+y^2]
theta=arctan(y/x), after which you must consider the given quadrant

See wikipedia: http://en.wikipedia.org/wiki/Polar_...rting_between_polar_and_Cartesian_coordinates

If you get an irrational answer in degree form, it's probably going to be irrational in radians form as well, e.g. tan-1[4/3]~53.130deg~.927r. in this case, there's no neat a*Pi+2nPi form, where a is rational and n is integer.

sphoenixee
 

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