College Trigonometry, 2011a

946 Applications of Trigonometry
6
r
y
4
θ = 4π 3
2
x
π
2
2π
3
π
4π
3
3π
2
2π
θ
−2
On the interval [ 4π
3 , 3π ]
2 , r returnstopositivevaluesandincreasesfrom0to2. Wehugthe
line θ = 4π 3
as we move through the origin and head towards the negative y-axis.
6
r
y
4
θ = 4π 3
2
x
π
2
2π
3
π
4π
3
3π
2
2π
θ
−2
As we round out the interval, we find that as θ runs through 3π 2
to 2π, r increases from 2 out
to 6, and we end up back where we started, 6 units from the origin on the positive x-axis.
6
r
y
4
2
x
−2
π
2
2π
3
π
4π
3
3π
2
2π
θ
θ runs from 3π 2
to 2π