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