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