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AonZ

Eliminate A from each pair of parametric equations x = 2tan( A/2) y = cosA

  • 11 months ago
  • 11 months ago

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  1. jdoe0001
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    $$\large{ 2 tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-cos(a)}{sin(a)}}\\ \color{red}{y} = \color{blue}{cos(a)} \ \ \ thus\\ 2tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-y}{sin(a)}} \implies \pmatrix{\frac{2-2y}{sin(a)}}\\ x=\frac{2-2y}{sin(a)} \implies \color{blue}{sin(a)} = \color{red}{\frac{2-2y}{x}} } $$

    • 11 months ago
  2. jdoe0001
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    then just use the identity of \(\large sin^2+cos^2 =1\) to get your equation

    • 11 months ago
  3. AonZ
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    how does \[{ 2 \tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-\cos(a)}{\sin(a)}}\\ }\]

    • 11 months ago
  4. jdoe0001
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    http://www.freemathhelp.com/images/halfangles.png half-angle identities, check your textbook formulas, or a formula cheatsheet you may have

    • 11 months ago
  5. jdoe0001
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    the picture there shows 2 for tangent, there are 3, at least on my sheet :)

    • 11 months ago
  6. AonZ
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    ok thanks i got it :)

    • 11 months ago
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