Finding the Coordinates of a Point Using Rectangular and Polar Formulas

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SUMMARY

The discussion focuses on converting rectangular coordinates (x, y) to polar coordinates (r, theta) using the formulas r = sqrt(x^2 + y^2) and theta = arctan(y/x). Given x = 7 and theta = 52 degrees, the correct approach involves solving for r using the equation x = rcos(theta) and subsequently determining y with y = rsin(theta). The user initially misassumed r to be equal to x, leading to an incorrect value for y. The correct method allows for accurate calculation of both r and y.

PREREQUISITES
  • Understanding of rectangular and polar coordinate systems
  • Familiarity with trigonometric functions (sine, cosine, arctangent)
  • Basic algebra skills for solving equations
  • Knowledge of the Pythagorean theorem
NEXT STEPS
  • Learn how to convert between rectangular and polar coordinates in various contexts
  • Study the applications of trigonometric functions in coordinate transformations
  • Explore advanced topics in polar coordinates, such as area and volume calculations
  • Practice solving problems involving multiple equations with two unknowns
USEFUL FOR

Students studying mathematics, particularly those focusing on geometry and trigonometry, as well as educators looking for clear examples of coordinate transformations.

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Homework Statement



The rectangular and polar coordinates of a point are (x,y) and (r,theta) where x = 7 and theta = 52 degrees. Determine r and y.

Homework Equations



r = srt(x^2 + y^2)
theta = arctan(y/x)
x = rcos(theta)
y = rsin(theta)

The Attempt at a Solution



I tried to assume that r and x would be the same, so I let r = 7, which would then make y = 5.5. But that's wrong. What else can possibly be done?
 
Last edited:
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2 equations, 2 unknowns

Use:
x=rcos(theta) eqn. 1
y=rsin(theta) eqn. 2

Since you know what x and theta are you can solve for r in eqn. 1.

Then once you know r you can plug that into eqn. 2 and solve for y.
 
Haha, nice. I was having one of those mental blocks that just would not allow me to think of that. Thanks.
 

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