Start by graphing the functions: PICTURE: graph them We can see that they intersect at two places. Set the equations equal: cosθ = sinθ This is true when θ = \frac{π}{4}. Then cosθ = sinθ = \frac{\sqrt2}{2}. One of our points of intersection is (r,θ) = (\frac{\sqrt2}{2}, \frac{π}{4}). We can see from the picture that these graphs also intersect at the origin, but we can't find that by solving the equation cosθ = sinθ because different values of θ make cosθ and sinθ equal to 0. This doesn't matter since the point (0,θ) is the same point no matter what θ is. PICTURE polar funcs 30 We may as well call the point *r* = 0 and not worry about θ. This point, *r* = 0, is the second intersection point. |