For t > 0, a particle moves along the curve x = a + b sin kt, y = a + b cos kt,
ID: 2849892 • Letter: F
Question
For t > 0, a particle moves along the curve x = a + b sin kt, y = a + b cos kt, where a, b, and k are positive constants.
(a)
(b) What is the effect on the curve of the following changes?.a,a+b
(i) increasing b
moves the center away from the origin along y = x
increases the radius
makes the particle move slower and increases the period
makes the particle move faster and reduces the period
makes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively
(ii) increasing a
moves the center away from the origin along y = x
increases the radius
makes the particle move slower and increases the period
makes the particle move faster and reduces the period
makes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively
(iii) increasing k
moves the center away from the origin along y = x
increases the radius
makes the particle move slower and increases the period
makes the particle move faster and reduces the period
makes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively
(iv) setting a and b equal
moves the center away from the origin along y = x
increases the radius
makes the particle move slower and increases the period
makes the particle move faster and reduces the period
makes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively
Explanation / Answer
x = a + b sin kt, y = a + b cos kt
x -a = b sin kt, y - a = b cos kt
(x-a)2 = b2 sin2 kt ,(y - a)2 = b2 cos2 kt
(x-a)2+(y-a)2= b2 sin2 kt + b2 cos2 kt
(x-a)2+(y-a)2= b2 (sin2 kt + cos2 kt)
(x-a)2+(y-a)2=b2
(b) What is the effect on the curve of the following changes?.a,a+b
(i) increasing b
increases the radius
(ii) increasing a
moves the center away from the origin along y = x
(iii) increasing k
makes the particle move faster and reduces the period
(iv) setting a and b equal
makes the curve touch both the x- and y-axes at the points (a, 0) and (0, a), respectively