## Calculus

### Parametric Equations and Polar Coordinates

This unit has additional topics covered later in a first-year calculus courses, including arc length, polar coordinates and graphs, and parametric functions. Polar coordinates are an alternative coordinate system for the plane that many students do not become familiar with until calculus. Parametric functions (x(t),y(t)) allow for the definition of curves that can trace out virtually any path in the plane, including both function graphs y = f(x) and polar graphs r = f(?)

### Calculus: Parametric Equations and Polar Coordinates Activities

Title Type

#### Polar Necessities

Students graphically and algebraically find the slope of the tangent line at a point on a polar graph.

• 3466

#### Gateway Arc Length

Investigate the arc length of the Gateway Arch, using the Pythagorean Theorem to approximate and using Calculus to find the exact solution. Students also solve arc length questions.

• 3033

#### Polar Graphs

Relate polar coordinates to rectangular coordinates and plot polar functions.

• 5244

#### Parametric Races & Slopes

Students will study the motion of two points and use calculus to determine the velocity and acceleration. The slope of parametric equations will be determined.

• 2968