Polar Coordinates (r,θ - University of Massachusetts Amherst

134 Pages·2007·1.7 MB·English

r = distance from the origin
and
θ ∈ [0,2π) is the counter-clockwise angle.
We make the convention
(−r,θ) = (r,θ + π).
Polar Coordinates (r,θ)
Polar Coordinates (r,θ) in the plane are described
by
and
θ ∈ [0,2π) is the counter-clockwise angle.
We make the convention
(−r,θ) = (r,θ + π).
Polar Coordinates (r,θ)
Polar Coordinates (r,θ) in the plane are described
by
r = distance from the origin
We make the convention
(−r,θ) = (r,θ + π).
Polar Coordinates (r,θ)
Polar Coordinates (r,θ) in the plane are described
by
r = distance from the origin
and
θ ∈ [0,2π) is the counter-clockwise angle.
Polar Coordinates (r,θ)
Polar Coordinates (r,θ) in the plane are described
by
r = distance from the origin
and
θ ∈ [0,2π) is the counter-clockwise angle.
We make the convention
(−r,θ) = (r,θ + π).
Polar Coordinates (r,θ)
Polar Coordinates (r,θ) in the plane are described
by
r = distance from the origin
and
θ ∈ [0,2π) is the counter-clockwise angle.
We make the convention
(−r,θ) = (r,θ + π).
(cid:16) π(cid:17) (cid:16) π(cid:17) (cid:16) π(cid:17)
(a) 1,5 (b) (2,3π) (c) 2,−2 (d) −3,3
4 3 4
Solution The points are plotted in Figure 3. In part (d) the point
(cid:0)−3,3π(cid:1) is located three units from the pole in the fourth
4
quadrant because the angle 3π is in the second quadrant and
4
r = −3 is negative.
Plotting points
Example
Plot the points whose polar coordinates are given.
Solution The points are plotted in Figure 3. In part (d) the point
(cid:0)−3,3π(cid:1) is located three units from the pole in the fourth
4
quadrant because the angle 3π is in the second quadrant and
4
r = −3 is negative.
Plotting points
Example
Plot the points whose polar coordinates are given.
(cid:16) π(cid:17) (cid:16) π(cid:17) (cid:16) π(cid:17)
(a) 1,5 (b) (2,3π) (c) 2,−2 (d) −3,3
4 3 4
In part (d) the point
(cid:0)−3,3π(cid:1) is located three units from the pole in the fourth
4
quadrant because the angle 3π is in the second quadrant and
4
r = −3 is negative.
Plotting points
Example
Plot the points whose polar coordinates are given.
(cid:16) π(cid:17) (cid:16) π(cid:17) (cid:16) π(cid:17)
(a) 1,5 (b) (2,3π) (c) 2,−2 (d) −3,3
4 3 4
Solution The points are plotted in Figure 3.
Plotting points
Example
Plot the points whose polar coordinates are given.
(cid:16) π(cid:17) (cid:16) π(cid:17) (cid:16) π(cid:17)
(a) 1,5 (b) (2,3π) (c) 2,−2 (d) −3,3
4 3 4
Solution The points are plotted in Figure 3. In part (d) the point
(cid:0)−3,3π(cid:1) is located three units from the pole in the fourth
4
quadrant because the angle 3π is in the second quadrant and
4
r = −3 is negative.
Plotting points
Example
Plot the points whose polar coordinates are given.
(cid:16) π(cid:17) (cid:16) π(cid:17) (cid:16) π(cid:17)
(a) 1,5 (b) (2,3π) (c) 2,−2 (d) −3,3
4 3 4
Solution The points are plotted in Figure 3. In part (d) the point
(cid:0)−3,3π(cid:1) is located three units from the pole in the fourth
4
quadrant because the angle 3π is in the second quadrant and
4
r = −3 is negative.