Question Detail
Question
Given that x = a sin t, y = a cos t, find the first derivative y'.
Correct Answer
Option A is the correct answer.
Detailed Explanation
To find y' = dy/dx, we use the chain rule for parametric equations: dy/dx = (dy/dt) / (dx/dt).Given x = a sin t, dx/dt = a cos t.Given y = a cos t, dy/dt = -a sin t.Therefore, dy/dx = (-a sin t) / (a cos t) = -tan t.
Hint
Remember the chain rule for parametric differentiation: dy/dx = (dy/dt) / (dx/dt).