Unformatted text preview: location coterminal with 240◦ . Hence,
our answer here is (−2, 60◦ ). We check our answers by plotting them.
Pole
θ = −120◦ P (2, −120◦ ) Pole θ = 60◦ P (−2, 60◦ ) π
π
2. We plot −4, 76 by ﬁrst moving 4 units to the left of the pole and then rotating 76 radians.
Since r = −4 < 0, we ﬁnd our point lies 4 units from the pole on the terminal side of π .
6 P −4, Pole θ= Pole 7π
6 7π
6 11.4 Polar Coordinates 785 To ﬁnd alternate descriptions for P , we note that the distance from P to the pole is 4 units, so
any representation (r, θ) for P must have r = ±4. As we noted above, P lies on the terminal
side of π , so this, coupled with r = 4, gives us 4, π as one of our answers. To ﬁnd a diﬀerent
6
6
representation for P with r = −4, we may choose any angle coterminal with the angle in the
π
π
π
original representation of P −4, 76 . We pick − 56 and get −4, − 56 as our second answer. P 4,
θ= π
6 π
θ = − 56 π
P −4, − 56 π
6 Pole Pole π
3. To plot P 117, − 52 , we move alon...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details