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A curve is defined by the parametric equations $x = ext{cos} heta$ and $y = ext{sin} heta$ where $0 leq heta leq 2 ext{π}$ - AQA - A-Level Maths: Pure - Question 1 - 2022 - Paper 1

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A-curve-is-defined-by-the-parametric-equations---$x-=--ext{cos}--heta$-and-$y-=--ext{sin}--heta$-where-$0--leq--heta--leq-2-ext{π}$-AQA-A-Level Maths: Pure-Question 1-2022-Paper 1.png

A curve is defined by the parametric equations $x = ext{cos} heta$ and $y = ext{sin} heta$ where $0 leq heta leq 2 ext{π}$. Which of the options shown bel... show full transcript

Worked Solution & Example Answer:A curve is defined by the parametric equations $x = ext{cos} heta$ and $y = ext{sin} heta$ where $0 leq heta leq 2 ext{π}$ - AQA - A-Level Maths: Pure - Question 1 - 2022 - Paper 1

Step 1

Identify the parametric equations

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Answer

The given parametric equations are:

  • x=extcoshetax = ext{cos} heta
  • y=extsinhetay = ext{sin} heta

Step 2

Find the Cartesian equation

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Answer

To eliminate the parameter heta heta, we can use the Pythagorean identity: extcos2heta+extsin2heta=1 ext{cos}^2 heta + ext{sin}^2 heta = 1 Substituting xx and yy into this identity results in: x2+y2=1x^2 + y^2 = 1

Step 3

Select the correct option

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Answer

Among the options given, the correct Cartesian equation is: x2+y2=1x^2 + y^2 = 1

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