Unit 9: Parametric, Polar and Vector Functions

For [math], [math], what is [math]?

Find the area enclosed by the polar curve [math] (a circle of radius 2).

Find the area of one petal of the rose curve [math].

A particle has position vector [math]. Find the speed at [math].

Convert the polar equation [math] to rectangular form.

A particle moves in the [math]-plane with [math] and [math]. The slope [math] at [math] is

The speed of a particle with position [math] at [math] is

The arc length of the curve [math], [math] from [math] to [math] is given by

The area enclosed by one petal of [math] is

The slope of the tangent line to the polar curve [math] at [math] can be found using

A particle has position vector [math]. The acceleration vector at [math] is

The area enclosed by the polar curve [math] (a cardioid) is

Find the speed of a particle with [math], [math] at any time [math].

Find the area enclosed by the polar curve [math].

A particle moves along [math], [math]. Find [math] at [math].

Convert the polar point [math] to rectangular coordinates.

Find the arc length of [math], [math] from [math] to [math].

For [math], find [math] at [math].

Find [math] for [math], [math].

The position of a particle is [math]. Find the speed at [math].

A particle moves in the xy-plane with [math] and [math]. What is the speed of the particle at [math]?

The area enclosed by the polar curve [math] is

For the parametric curve [math], [math], which equation describes the curve in rectangular form?

A curve is defined parametrically by [math] and [math]. At what value of [math] does the curve have a horizontal tangent?

The area enclosed by the polar curve [math] is

A particle moves in the xy-plane with position [math] for [math]. What is the speed of the particle at [math]?