1 / 12

Today in Precalculus

Today in Precalculus. Go over homework Connection between polar and rectangular graphs of trig functions Notes: More on Graphs of Polar Equations Homework. y = 4cos(2x) b. y = 2 + 2sin(x) Range: [-4,4] Range: [0,4] Max. r value:4 Max r value: 4. Conclusions.

amelia
Download Presentation

Today in Precalculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Today in Precalculus • Go over homework • Connection between polar and rectangular graphs of trig functions • Notes: More on Graphs of Polar Equations • Homework

  2. y = 4cos(2x) b. y = 2 + 2sin(x) Range: [-4,4] Range: [0,4] Max. r value:4 Max r value: 4

  3. Conclusions Rose curve equations are sin or cos waves in rectangular form with changes only to the amplitude and period. Therefore the range of a rose curve is symmetric to zero. Limacon curve equations are sin or cos waves in rectangular form with changes to the amplitude and vertical shift. Therefore the range of a limacon curve is not symmetrical to zero.

  4. What happens when the “a” is negative in a rose curve? r = 2 sin3θ r = -2sin3θ If n is odd, the graph is reflected over the x-axis. If n is even, the graph doesn’t change. The points plot in a different order.

  5. What happens when the “a” is negative in a rose curve? r = 2 cos3θ r = -2cos3θ If n is odd, the graph is reflected over the y-axis. If n is even, the graph doesn’t change. The points plot in a different order.

  6. What happens when the “b” is negative in a limacon curve? r = 1 + 2sinθ r = 1 – 2 sinθ When b is positive, the majority of the curve is around the positive y-axis When b is negative, the majority of the curve is around the negative y-axis.

  7. What happens when the “b” is negative in a limacon curve? r = 1 + 2cosθ r = 1 – 2cosθ When b is positive, the majority of the curve is around the positive x-axis When b is negative, the majority of the curve is around the negative x-axis.

  8. Rose curve Petal length = 3 Petals on all axis, so cos 4 petals so n =2 r = 3cos2θ

  9. Dimpled limacon Majority of graph over negative x-axis, so negative cos Max r value = 5 = a+b a – b = 1 (where the dimple is) b=2 a=3 r = 3 – 2cosθ

  10. Limacon with inner loop Majority of graph over negative y-axis, so negative sin Max r value = 5 = a+b a – b = -1 (where the loop touches) r = 2 – 3sinθ

  11. Rose curve Petal length = 2 One petal on y-axis, so sin Five petals, n = 5 5 petals should have one petal on positive y-axis, so sin negative r = -2sin5θ

  12. Homework Worksheet Polar Quiz Friday, April 11

More Related