rectangular (cartesian) coordinates plot a point by moving left/right and up/down (making a...
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![Page 1: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/1.jpg)
Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle)
Polar coordinates find the same point in a different way
r = distance from the origin (radius)θ = angle with positive x-axis
Polar Coordinates
![Page 2: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/2.jpg)
Ex. The Cartesian coordinates of a point are given, find the polar coordinates.
a) (0,1)
b)
c)
2 22 2,
2 3,2
![Page 3: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/3.jpg)
cos
sin
x r
y r
2 2 2
tan yx
x y r
Polar Rect Rect Polar
Ex. The polar coordinates of a point are given, find the Cartesian coordinates.
a) (2,π)
b) 63,
![Page 4: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/4.jpg)
Ex. Find the polar equation for the curve.a) x2 + y2 = 3y
b) x3y2 + ln y = 3
![Page 5: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/5.jpg)
Ex. Find the Cartesian equation for the curve.a) r = cos θ
b) sin θ = r2 cos θ
![Page 6: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/6.jpg)
Ex. Sketch the polar equation r = 3
6
4
2
- 2
- 4
- 6
- 5 5
![Page 7: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/7.jpg)
Ex. Sketch the polar equation θ =
6
4
2
- 2
- 4
- 6
- 5 5
3
![Page 8: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/8.jpg)
Ex. Sketch the polar equation r = sec θ.
6
4
2
- 2
- 4
- 6
- 5 5
![Page 9: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/9.jpg)
Ex. Sketch the polar equation r = 2cos5θ
6
4
2
- 2
- 4
- 6
- 5 5
![Page 10: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/10.jpg)
For the function r = f (θ),
cos sin
cos sin
dyd
dxd
f fdy
dx f f
Ex. Find the points of horizontal and vertical tangency on the graph r = sin θ, 0 ≤ θ ≤ 2.
![Page 11: Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different](https://reader036.vdocument.in/reader036/viewer/2022062314/56649e995503460f94b9be57/html5/thumbnails/11.jpg)
Pract.
1. Convert the polar point to Cartesian.
2. Sketch the curve r = 2cos θ.
3. Find the slope of the tangent line to r = 1 + sin θ when θ =
1, 3
32,
13