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Class 12 Inverse Trigonometric Functions · Short Answer2 Marksinverse_function_graphs

Class 12 Maths · Inverse Trigonometric Functions · Short Answer #55

Draw \(y=\cos^{-1}x\) for \(x\in[-1,0]\), and state its range.
y=arccos x for −1≤x≤0, with range [π/2,π]. Both endpoints are closed.
y=arccos x for −1≤x≤0, with range [π/2,π]. Both endpoints are closed.

✅ Step-by-Step Solution

Final Answer: [π/2,π]
  1. The endpoint values are arccos(−1)=π and arccos0=π/2.
  2. Arccosine is continuous and strictly decreasing on [−1,0]; draw the curve between (−1,π) and (0,π/2), both endpoints closed. The attached SVG gives this plot.
  3. Therefore the range is [π/2,π].

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The endpoint values are arccos(−1)=π and arccos0=π/2.
  • [1 mark] Arccosine is continuous and strictly decreasing on [−1,0]; draw the curve between (−1,π) and (0,π/2), both endpoints closed. The attached SVG gives this plot.
  • [0.5 marks] Therefore the range is [π/2,π].

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