polar!...
TRANSCRIPT
![Page 1: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/1.jpg)
POLAR CURVES
![Page 2: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/2.jpg)
SPECIFIC OBJECTIVES: At the end of the lesson, the student is expected to be
able to: • define polar coordinates. • plot points polar coordinates. • write and sketch the graphs of polar equa=ons. • convert polar to rectangular and vice versa.
![Page 3: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/3.jpg)
![Page 4: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/4.jpg)
![Page 5: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/5.jpg)
Examples: Plot the given points on a polar coordinate system. a. P (3, 45°)
b. P (3, –60°)
![Page 6: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/6.jpg)
c. P (–3, 220°) d. P (-‐3, –75°)
![Page 7: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/7.jpg)
RELATIONS BETWEEN RECTANGULAR AND POLAR COORDINATES
The transforma=on formulas that express the rela=onship between rectangular coordinates and polar coordinates of a point are as follows:
and
Also, ; ;
![Page 8: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/8.jpg)
![Page 9: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/9.jpg)
2. Express the rectangular coordinates (-‐4, 3) in terms of polar coordinates.
![Page 10: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/10.jpg)
![Page 11: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/11.jpg)
![Page 12: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/12.jpg)
![Page 13: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/13.jpg)
![Page 14: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/14.jpg)
Cardiod Limacon
![Page 15: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/15.jpg)
Eight – leaf Rose Three – leaf Rose
![Page 16: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/16.jpg)
Spiral of Archimedes Logarithmic Spiral
![Page 17: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/17.jpg)
Lemniscate
![Page 18: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/18.jpg)
30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° 360°
1 0.87 0.5 0 -‐0.5 -‐0.87 -‐1 -‐0.87 -‐0.5 0 0.5 0.87 1
2 1.73 1 0 -‐1 -‐1.73 -‐2 -‐1.73 -‐1 0 1 1.73 2
r 3 2.73 2 1 0 -‐0.73 -‐1 -‐0.73 0 1 2 2.73 3
![Page 19: POLAR! CURVES!polpinit/classes/math1/Lecture...SPECIFIC!OBJECTIVES:!!!Atthe!end!of!the!lesson,!the!studentis!expected!to!be! able!to:!! •define!polar!coordinates.! •plotpoints!polar!coordinates.!](https://reader036.vdocument.in/reader036/viewer/2022071608/614710e2f4263007b1359478/html5/thumbnails/19.jpg)