Find the Cartesian equation for .

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SUMMARY

The Cartesian equation for the polar equation r = 4sec(θ) is x = 4, representing a vertical line where y can take any value. The conversion process involves substituting sec(θ) with 1/cos(θ), leading to the conclusion that x remains constant at 4. The original problem does not require finding r, y, or θ, as the Cartesian form is already established. This discussion clarifies that the focus should be on the Cartesian representation rather than additional polar coordinates.

PREREQUISITES
  • Understanding of polar coordinates and their conversion to Cartesian coordinates.
  • Familiarity with trigonometric functions, specifically secant and cosine.
  • Knowledge of basic algebraic manipulation and equation solving.
  • Ability to interpret and analyze mathematical problem statements.
NEXT STEPS
  • Study the conversion process from polar to Cartesian coordinates in detail.
  • Learn about the properties of vertical lines in Cartesian geometry.
  • Explore trigonometric identities, particularly the relationship between secant and cosine.
  • Practice additional polar equations and their Cartesian equivalents for better comprehension.
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Students studying mathematics, particularly those focusing on calculus and coordinate geometry, as well as educators teaching these concepts.

Calpalned
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Homework Statement


r = 4sec(θ)

Homework Equations


x2 + y2 = r2
y = rsin(θ)
x = rcos(θ)

The Attempt at a Solution


Given that r = 4sec(θ), I replaced sec(θ) with 1/cos(θ) and got x = 4. The problem is that I'm not sure if that's the final answer because I have been unable to find r, y or θ.
 
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Is that the whole problem statement? We can't help if we don't see the complete statement.

Did they expect you plot it or convert it to xy coordinates?

If it's a conversion to xy then whatif you place the secant on the other with the r?
 
Calpalned said:

Homework Statement


r = 4sec(θ)

Homework Equations


x2 + y2 = r2
y = rsin(θ)
x = rcos(θ)

The Attempt at a Solution


Given that r = 4sec(θ), I replaced sec(θ) with 1/cos(θ) and got x = 4. The problem is that I'm not sure if that's the final answer because I have been unable to find r, y or θ.

The cartesian form of r = 4sec(θ) IS x=4. It's a vertical line y can be anything. Why do you think you should be able to find r, y or θ?
 

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