Math Problem Statement

Convert the equations y = 5 and x = 5 to polar form using variables r and θ.

Solution

To convert the given equations y=5y = 5 and x=5x = 5 into polar form, we use the following polar coordinate relationships:

  1. x=rcosθx = r\cos\theta
  2. y=rsinθy = r\sin\theta

1. Conversion of y=5y = 5:

Using y=rsinθy = r\sin\theta, substitute y=5y = 5: rsinθ=5r\sin\theta = 5 Thus, the polar form is: r=5sinθorr=5cscθr = \frac{5}{\sin\theta} \quad \text{or} \quad r = 5\csc\theta

2. Conversion of x=5x = 5:

Using x=rcosθx = r\cos\theta, substitute x=5x = 5: rcosθ=5r\cos\theta = 5 Thus, the polar form is: r=5cosθorr=5secθr = \frac{5}{\cos\theta} \quad \text{or} \quad r = 5\sec\theta

If you have any additional questions or need further details about polar coordinate conversions, feel free to ask!

Related Questions:

  1. How do you convert general linear equations to polar form?
  2. What is the significance of the csc and sec functions in polar equations?
  3. How does polar form simplify graphical representation of lines?
  4. Can polar forms r=5cscθr = 5\csc\theta and r=5secθr = 5\sec\theta be visualized in terms of their graphs?
  5. How does converting to polar form help in understanding angular relationships?

Tip:

Always remember that polar forms can sometimes require restrictions

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Math Problem Analysis

Mathematical Concepts

Polar Coordinates
Conversion between Cartesian and Polar forms

Formulas

x = r * cos(θ)
y = r * sin(θ)

Theorems

Trigonometric identities in polar coordinates

Suitable Grade Level

Grades 10-12