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
Question 1
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=extcosheta
y=extsinheta
Step 2
Find the Cartesian equation
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Answer
To eliminate the parameter heta, we can use the Pythagorean identity:
extcos2heta+extsin2heta=1
Substituting x and y into this identity results in:
x2+y2=1
Step 3
Select the correct option
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Answer
Among the options given, the correct Cartesian equation is:
x2+y2=1
