Proof: 5.25
Proof: 5.25
Use algebra and a graph to find all points where the curves and intersect.
Proof:
Proof: Consider the following polar equations: and . Furthermore, note that . Now, we shall notice the following:
-- [trig identity: ]
Note that we can now find for which and . Consider the following:
First consideration:
.
Second consideration:
.
Thus, we know that are all values for theta for which and intersect. If we wish to represent them as points, we can substitute our values for theta into either equation and get that the points are as follows:
A = (, 1.5)
B = (, 1.5)
C = (, -3).
Note that (0, 0) is not a point of intersection because substituting 0 in for theta yields two different values of r.