Question

Consider the following vector equation.

r(t) = 3 sin(t)i − 2 cos(t)j
(a) Find r ′(t). r ′(t) =

Answer 1

The derivative of the vector equation r(t) = 3 sin(t)i − 2 cos(t)j is r′(t) = 3 cos(t)i + 2 sin(t)j.

Step-by-step explanation:

To find the derivative of the vector equation r(t) = 3 sin(t)i − 2 cos(t)j, we take the derivative of each component separately. The derivative of sin(t) is cos(t), and the derivative of cos(t) is -sin(t). Therefore, r′(t) = 3 cos(t)i + 2 sin(t)j.