Math Problem Statement
sin(0,5t)=x cos(0,5t)=y, make it a cartesian equation by eliminating the parameter
Solution
To eliminate the parameter from the parametric equations:
we use the Pythagorean identity for sine and cosine:
Substituting and , we get:
Thus, the Cartesian equation is:
This represents a circle with a radius of 1, centered at the origin.
Would you like a more detailed explanation or examples? Here are five related questions to explore further:
- What if and with a different constant ?
- How does the parameter influence the parametric equations' behavior over time?
- How can we extend this method to eliminate parameters in other trigonometric forms?
- Can you derive the Cartesian equation if the parametric equations involve phase shifts, such as ?
- What does the equation represent geometrically in higher dimensions?
Tip: For trigonometric parametric equations, the Pythagorean identity is your key tool for eliminating parameters!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Parametric Equations
Pythagorean Identity
Formulas
sin^2(θ) + cos^2(θ) = 1
Theorems
Pythagorean Identity
Suitable Grade Level
Grades 9-12
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