Given is the parametric curve $K$ that satisfies $$\begin{cases}x=3\sin t \\ y=2\cos\left(t-\frac{1}{4}\pi\right)\end{cases}$$
How can you change the parametric equations if you want to turn the direction of movement? The answers say $t\mapsto t+\frac{1}{4}\pi$, but I don't understand why.. Could someone explain?
The curve is an ellipse shown below. As $t$ increases the position of the general point $(x,y)$ rotates in an anticlockwise direction.
The transformation $t \rightarrow t+\frac \pi 4$ keeps the curve the same. It also keeps the direction of movement the same (anticlockwise). What does change is that each point associated with a particular time moves around the curve in the direction of movement.