Question

Considering x = 2cos(t), y = 2sin(t), 0 ≤ t ≤ ..., what shape is traced out by x and y?

a) Circle
b) Ellipse
c) Parabola
d) Hyperbola

Answer 1

The equations x = 2cos(t) and y = 2sin(t) describe a circle with a radius of 2, centered at the origin, as they satisfy the equation of a circle x^2 + y^2 = 4.

Step-by-step explanation:

The shape traced out by the equations x = 2cos(t) and y = 2sin(t) for 0 ≤ t ≤ 2π is a circle. This can be demonstrated by using the trigonometric identity cos2(t) + sin2(t) = 1 to show that x2 + y2 = 4cos2(t) + 4sin2(t) = 4(cos2(t) + sin2(t)) = 4, which is the equation of a circle with a radius of 2 centered at the origin (0,0). Therefore, the correct answer is (a) Circle.