Q69 / 125 · BITSAT 2009 · Mathematics

The equation of tangent to the curve \(y=\sin x\) at the point \((\pi, 0)\) is

  • A
    \(x+y=0\)
  • Correct answer
    B
    \(x+y=\pi\)
  • C
    \(x-y=\pi\)
  • D
    \(x-y=0\)

Solution

\(y=\sin x \Rightarrow \frac{d y}{d x}=\cos x \Rightarrow\left(\frac{d y}{d x}\right)_{(\pi, 0)}=-1\) Therefore the equation of tangent at \((\pi, 0)\) is given by \(y-0=-1(x-\pi) \Rightarrow x+y=\pi\)

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

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