Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 3 + 2 cos(t), π/2 ≤ t ≤ 2π

The motion of the particle describes an ellipse.

Step-by-step explanation:

The characteristics of the motion of the particle is derived by eliminating in the parametric expressions. Since both expressions are based on trigonometric functions, we proceed to use the following trigonometric identity:

(1)

Where:

(2)

(3)

By (2) and (3) in (1):

(4)

The motion of the particle describes an ellipse.

last option: rhombus or kite

step-by-step explanation:

a kite and rhombus have the same shape. as we don't have any specific formula for the calculation of area of kite. the diagonals are used to calculate the area of a kite or rhombus.

the formula for area of rhombus is given by:

here, d_1 is the first diagonal and d_2 is the second diagonal.

so,

last option is the correct answer ..

the answer will be the last one