calc_tutorial_13_1_014

 
Problem Statement

{2,3,4,5}
{11,13,15,17}
pow(13,2)
{0}

The function r(t) traces a circle. Determine the radius, center of the circle, and plane containing the circle.

r(t) = 3i + (13 cos t)j + (13 sin t)k

 
Step 1

Question Sequence

Question 1

In order to determine the radius, center, and plane containing the circle, we must write the components of r(t) as parametric functions in (x, y, z). Given r(t) = 3i + (13 cos t)j + (13 sin t)k, write the appropriate parametric equations describing x(t), y(t), z(t).

x(t) =

y(t) = cos t

z(t) = sin t

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

To determine the radius of the circle, calculate y2(t) + z2(t) since y(t) and z(t) both contain the trigonometric functions which will parametrize the circle.

y2(t) + z2(t) = (13 cos t)2 + (13 cos t)2 = 169

State the radius of the circle parametrized by r(t).

radius =

Correct.
Incorrect.

 
Step 3

Question Sequence

Question 3

Since x(t) = 3 is a constant function, every point on the circle has x-component 3. This fixes the plane containing the circle.

Determine the plane containing the circle.

A.
B.
C.
D.
E.
F.
Correct.
Incorrect.

 
Step 4

Question Sequence

Question 4

Since the circle lies in the plane x = 3, the x-component of the center of the circle must be

x =

To determine the y- and z-components of the center of the circle defined by r(t), look at y2 + z2 = 132 from step 2. This is the equation of a circle with radius 13, centered at

(y, z) = (, )

Adding the third component, x = 3, does not affect the y- and z-components corresponding to the center of this circle.

State the center of the circle defined by r(t).

(x, y, z) = (, , )

Correct.
Incorrect.