Problem 47E

Derivatives Consider the following parametric curves.

a. Determine dy/dx in terms of t and evaluate it at the given value of t.

b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.

x = cos t, y = 8 sin t; t = π/2

Solution 47E

Step 1:

To obtain the derivative we need which we can also write as

Evaluating andseparately, we get

Putting the valuesand into evaluate , we get

.

Hence the value of is .

at is which means the tangent at this point is a horizontal line.