Math Problem Statement
Solution
To convert to rectangular form, we should think about the relationship between polar and rectangular coordinates.
For a line at an angle with the origin in polar coordinates, this angle corresponds to a line where the slope is determined by .
-
Calculate the Slope: Therefore, the line has a slope of .
-
Equation of the Line: In rectangular form, this is the line , since the angle in polar coordinates corresponds to the line where and have opposite signs with equal magnitudes (slope of ).
Answer:
The correct answer is: D.
Would you like further details or have any questions?
Here are five related questions for deeper understanding:
- How do you convert from polar to rectangular coordinates in general?
- What are some common angles and their corresponding slopes in rectangular form?
- Why does equal ?
- How would you find the rectangular form of a polar equation with a radius, such as ?
- What is the rectangular form of ?
Tip: When converting polar angles to rectangular equations, think about the trigonometric values of the angle, as they often determine the slope or relationship between and .
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Polar and Rectangular Coordinates
Trigonometry
Coordinate Conversion
Formulas
tan(θ) = y/x
Slope formula: m = tan(θ)
Theorems
Definition of Polar to Rectangular Conversion
Suitable Grade Level
Grades 10-12