If x = a(t − sin t) and y = a(1 − cos t), find dy/dx at t = π/2. A. 0 B. 1 C. −1 D. Does not exist Answer: B) 1 Explanation: dx/dt = a(1 − cos t), dy/dt = a sin t. dy/dx = sin t / (1 − cos t). At t = π/2, sin(π/2) = 1, cos(π/2) = 0. So dy/dx = 1/1 = 1.

imo class 12 continuity and differentiability

If x = a(t − sin t) and y = a(1 − cos t), find dy/dx at t = π/2.

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If x = a(t − sin t) and y = a(1 − cos t), find dy/dx at t = π/2.

Answer: B) 1

Explanation: dx/dt = a(1 − cos t), dy/dt = a sin t. dy/dx = sin t / (1 − cos t). At t = π/2, sin(π/2) = 1, cos(π/2) = 0. So dy/dx = 1/1 = 1.