Q224 / 270 · NDA 2012 (Phase 1) · Mathematics

If $y=\cos t$ and $x=\sin t$, then what is $\frac{d y}{d x}$ equal to?

  • A
    $x y$
  • B
    $x / y$
  • C
    $-y / x$
  • Correct answer
    D
    $-x / y$

Solution

$\frac{d y}{d t}=-\sin t, \frac{d x}{d t}=\cos t$ $\frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{-\sin t}{\cos t}=-\frac{x}{y}$.

Hence, the correct answer is option: 'D'.

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