Question

Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)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.)

Answer 1

Answer:

$x = 4\cdot \cos t$

$y = 1 + 4\cdot \sin t$

Step-by-step explanation:

The parametric equations are determined by determining the trigonometric expressions associated to each component. Let 16 the square of the hypotenuse of a right-angled triangle, of which one of its extremes is set on the center of the circle C(0, 1). Then:

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1$

By remembering the fundamental trigonometric identity ($\cos^{2} t + \sin^{2}t = 1$) and comparing it with each term, the parametric equations are finally found:

$x = 4\cdot \cos t$

$y = 1 + 4\cdot \sin t$