At how many places does the curve x = cos 3t, y = sin t cross the x-axis?
A)1
B)2
C)3
D)4
E)5
F)6
G)7
H)8

Question

Quizplus · Accepted Answer

To find the points where the curve crosses the x-axis, we need to find the values of t when y=0. From the given equation, we have y=sin(t), so sin(t)=0 when t=0, π, 2π, … (kπ, where k is an integer). 
Substituting these values of t into x=cos(3t), we get x=cos(0)=1, cos(3π)=-1, cos(6π)=1, ... 
So the curve crosses the x-axis at x=1 and x=-1. Therefore, the number of places where the curve crosses the x-axis is 2, which is option (B).

At How Many Places Does the Curve X = Cos