Calc practice.

[jeca86]

x=1+cos(theta), y=2cos(theta)-1

a) eliminate the parameter to find a cartesian equation of the curve.
b) sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

for the first part I got y=2x-3 Is this right?

 

[Unco]

a) Correct so far. Now you need to consider the range of f(theta)=cos(theta) to determine the domain and range of your function.

b) It depends on where we start. From theta=0 to theta=pi, f(theta)=cos(theta) decreases so x and y ..... . From theta=pi to theta=2pi f(theta)=cos(theta) increases.