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maddylaugh
26.11.2019 •
Mathematics
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.
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Ответ:
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![x_0 = 0, y_0 = 3, r = 4](/tpl/images/0391/1538/b9101.png)
Thus, the parametric equations are:
A similar problem is given at link
Ответ:
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]
Ответ: