Question
Download Solution PDFLet the slope of the curve y = sin-1 (cos x) be tan θ, then the value of θ in the interval (0, π) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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