Question

The function r(t)=6+11cos(t)+11sin()r(t)=6i+j+11sin(t)k traces a circle. Determine the:

a. Radius of the circle.
b. Center of the circle.
c. Plane containing the circle.
d. Circumference of the circle.

Answer 1

The function r(t)=6+11cos(t)+11sin(t) traces a circle. The radius of the circle is 11, the center is (6, 1, 0), it lies in the xy-plane, and the circumference is approximately 69.1 units.

Step-by-step explanation:

The function r(t)=6+11cos(t)+11sin()r(t)=6i+j+11sin(t)k traces a circle. To determine:

a. Radius of the circle:

The radius of the circle is the coefficient of the sine and cosine terms. In this case, the radius is 11.

b. Center of the circle:

The center of the circle is the constant term in the function. In this case, the center is (6, 1, 0).

c. Plane containing the circle:

The circle lies in the xy-plane, since the z-coordinate is always 0.

d. Circumference of the circle:

The circumference of a circle is given by the formula 2πr, where r is the radius. In this case, the circumference is 22π or approximately 69.1 units.