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Let the slope of the curve y = sin-1 (cos x) be tan θ, then the value of θ in the interval (0, π) is

  1. π/6
  2. π/4
  3. 3π/4
  4. -π/4

Answer (Detailed Solution Below)

Option 3 : 3π/4
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Detailed Solution

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Concept:

Formula:

  • cos-1 (cos x) = x
  • sin-1 (sin x) = x
  • Slope of the curve = tan θ = \(\rm \frac {dy}{dx}\)

 

Calculation:

Given: Slope = tan θ

y = sin-1 (cos x)

⇒ y = sin-1 (sin (π/2 -x))

⇒ y = π/2 – x                                        (∵ sin-1 (sin x) = x)

Differentiating both sides with respect to x, we get

\(\rm \frac {dy}{dx}\) = -1

As we know, Slope = \(\rm \frac {dy}{dx}\)

⇒ tan θ  = -1

∴ θ = 3π/4

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