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  2. AP Pre Calculus
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Explain how changing the parameter 't' affects a parametric curve.

Changing 't' traces the curve. Restricted domain of 't' means the graph has start and end points.

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Explain how changing the parameter 't' affects a parametric curve.

Changing 't' traces the curve. Restricted domain of 't' means the graph has start and end points.

Why are parametric functions useful for representing complex shapes?

They can represent circles, ellipses, and other complex shapes with a consistent set of equations, offering flexibility.

Why are parametric functions useful for animations?

By changing the parameter 't', we can make the curve move dynamically, creating animations and interactive graphics.

How does the domain of the parameter 't' affect the graph of a parametric function?

The domain of 't' determines the start and end points of the curve. A restricted domain results in a segment of the curve.

Parametric equation for a circle with center (h, k) and radius r?

x(t)=h+rcos⁡(t)x(t) = h + r \cos(t)x(t)=h+rcos(t), y(t)=k+rsin⁡(t)y(t) = k + r \sin(t)y(t)=k+rsin(t)

How to represent x and y using parameter t?

x=f(t)x = f(t)x=f(t), y=g(t)y = g(t)y=g(t)

How to eliminate the parameter 't' to find the Cartesian equation?

Solve one parametric equation for 't', then substitute into the other equation.

How to find the coordinates of a point on a parametric curve at a specific value of 't'?

Substitute the value of 't' into both parametric equations: x = f(t), y = g(t).

How to determine the start and end points of a parametric curve?

Use the domain restrictions on 't'. Plug the minimum and maximum values of 't' into the equations to find the (x, y) coordinates.