Points, Vectors, and Functions Exercises

Answer

• Graph the functions first:

• If we zoom in enough we can see that there are three points of intersection. One of these is the origin, r = 0.

• Set the functions equal and solve:

We didn't need to use   when finding the intersection of sin θ and cos θ, but we need it now because we have more points of intersection.When we have , and when we have . 

The points of intersection are

Answer

• First, draw the graph:

• It looks like we have three points of intersection again, and one of them is r = 0.To find the other two points we need to set the functions equal and solve for θ.

At these values of θ,

The points of intersection are

Answer

• Graph the functions:

• 
• There are two points of intersection in the first quadrant. We set the functions equal and solve for θ.

The points of intersection are