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 y' = dy/dx for parametric equations, we use the chain rule: dy/dx = (dy/dt) / (dx/dt).First, find dx/dt:dx/dt = d/dt (a sin t) = a cos t.Next, find dy/dt:dy/dt = d/dt (a cos t) = -a sin t.Now, divide dy/dt by dx/dt:dy/dx = (-a sin t) / (a cos t) = - (sin t / cos t) = -tan t.
Hint
Remember the chain rule for parametric differentiation: dy/dx = (dy/dt) / (dx/dt).