Stitz-Zeager_College_Algebra_e-book

# N b use theorem 1116 to show that eix einx for any

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ouraged to check these results algebraically and geometrically. 3. Proceeding as above, we ﬁrst graph r = 3 and r = 6 cos(2θ) to get an idea of how many intersection points to expect and where they lie. The graph of r = 3 is a circle centered at the origin with a radius of 3 and the graph of r = 6 cos(2θ) is another four-leafed rose.12 y 6 3 −6 −3 3 6 x −3 −6 r = 3 and r = 6 cos(2θ ) It appears as if there are eight points of intersection - two in each quadrant. We ﬁrst look to see if there any points P (r, θ) with a representation that satisﬁes both r = 3 and r = 6 cos(2θ). π For these points, 6 cos(2θ) = 3 or cos(2θ) = 1 . Solving, we get θ = π + πk or θ = 56 + πk 2 6 for integers k . Out of all of these solutions, we obtain just four distinct points represented π π by 3, π , 3, 56 , 3, 76 and 3, 11π . To determine the coordinates of the remaining four 6 6 points, we have to consider how the representations of the points of intersection can diﬀer. We know from Section 11.4 that if (r, θ) and (r , θ ) represent the same point and r = 0, then either r = r...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online