TAN θ = dy/dx Calculation:Given: Slope = tan θ y = cos-1 (sin x)⇒ y = cos-1 (cos (π/2 -x))⇒ y = π/2 –x (∵ cos-1 (cos x) = x)Differentiating both SIDES with RESPECT to x, we getdy/dx = -1So, Slope = dy/dx⇒ tan θ = -1∴ θ = 3π/4

"> TAN θ = dy/dx Calculation:Given: Slope = tan θ y = cos-1 (sin x)⇒ y = cos-1 (cos (π/2 -x))⇒ y = π/2 –x (∵ cos-1 (cos x) = x)Differentiating both SIDES with RESPECT to x, we getdy/dx = -1So, Slope = dy/dx⇒ tan θ = -1∴ θ = 3π/4

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

UPSEE Calculus in UPSEE 11 months ago

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Concept:cos-1 (cos x) = xSlope = TAN θ = dy/dx Calculation:Given: Slope = tan θ y = cos-1 (sin x)⇒ y = cos-1 (cos (π/2 -x))⇒ y = π/2 –x (∵ cos-1 (cos x) = x)Differentiating both SIDES with RESPECT to x, we getdy/dx = -1So, Slope = dy/dx⇒ tan θ = -1∴ θ = 3π/4

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Posted on 01 Dec 2024, this text provides information on UPSEE related to Calculus in UPSEE. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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