Find parametric equations for the path of a particle that moves along the circle x2 + (y − 3)2 = 16 in the manner described. (enter your answer as a comma-separated list of equations. let x and y be in terms of t.) (a) once around clockwise, starting at (4, 3). 0 ≤ t ≤ 2π.

The parametric equations for the circle are:

The equation of a circle of radius r and center is given by:

The parametric equations, considering a counter-clockwise movement, are given by:

Considering a clockwise movement, t is replaced by -t, thus:

However, considering the even cosine function and the odd sine function, we have that:

Hence:

In this problem, the circle's equation is given by:

Hence

Thus, the parametric equations are:

A similar problem is given at link

and t ∈ [0,2π]

Step-by-step explanation:

The standard equation for circle is:

Comparing our equation with standard

h= 0,

k= 3

r= 4 (as in standard r², so r =√ r²)

Required:

Parametric equations of the circle

Formula:

Putting values of r and h and k we get

As we need to start the object at (4,3)

x(0) = 4 and y(0) = 3

and the period is 2π

As the rotation is starting clock wise we will invert the value of t i.e -t

and t ∈ [0,2π]

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: