lesson 5-polar graphs day 1.notebook · lesson 5polar graphs day 1.notebook 10 february 12, 2018...
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Lesson 5Polar Graphs Day 1.notebook
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February 12, 2018
.P.T.S
#1, 4, 5 #2, 3, 6
.Q.W .R
Homework Answers
#7. y = (2/3)x + 1
#8. P( , 3√32
32 ) ( , ‐9√343
4 ) S ( , √22T ‐√2
2 )
Lesson 5Polar Graphs Day 1.notebook
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.
#9 #10
.
.
#13 #14
.
15) ≈ 6.16
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#16 and #17 #18‐21
r = 6
r = ‐5
θ = 2
θ = ‐1
θ = 17πθ = ‐5π
22. (10, ‐π )4
(5√2, ‐5√2) ≈ (7.07, ‐7.07)
23. (‐9, 5π )6
(9√3, ‐9) ≈ (7.79, ‐4.5)2 2
24. (2, 1.67) ≈ (‐.20, 1.99)
25. (1, 1) ≈ (.54, .84)
Lesson 5Polar Graphs Day 1.notebook
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26. (5, ‐5 ) (5√2, 7π)4
27. (0, 9) (9, π )2
28. (‐4, 4√3) (8, 2π )3
29. (‐1, √3) (1, 2π )32 2
DO NOW!
Graph r=4cosθ and r=6sinθ
State the diameter and symmetry with respect to which axis.
Lesson 5Polar Graphs Day 1.notebook
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Goals~To play with our calculators to graph polar equations~
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February 12, 2018
Try graphing r = a sin O and r = a cos O for various positive and neagative values for a.
~ ~
What shapes are these graphs?
How does the value of a relate to the graphs?
U4 L5: Graphing Polar Equations
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Limacons are polar graphs of the form
r = a + b cos O and r = a + b sin O.~ ~
Limacon is french for a type of snail
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February 12, 2018
Describe what the limacon looks like when a < b, when a > b, and when a = b.
Graph: r=2+3cosθ r=23cosθ xintercepts
b±ayintercepts
±aGraph: r=4+2cosθ r=4+2cosθ
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February 12, 2018
Cartoids are special forms of limacons where a and b are equal.
What happens when the equation includes sin O vs. cos O?~ ~
r = 3+3sinθ
How do you make heart right side up??
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February 12, 2018
Roses are polar graphs of the form r = a cos n O and r = a sin n O ~ ~
Change the values of a and n and see what happens.
What happens when the equation contains cos vs. sin?
Roses:
r = a cos n θ r = a sin n θ
if n is odd, we get petals.
if n is even, we get petals.
Graph each and fill in the blanks in the sentences below.
r = 3 cos 2 θr = 4 cos 4 θ
r = 3 cos 3θr = 3 cos 5θ
r= 5 sin 3θr = 2 sin 6θ
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An Archimedean spiral (also arithmetic spiral), is a spiral named after the 3rdcenturyBC Greek
mathematician Archimedes; it is the locus of points corresponding to the locations over time of a point
moving away from a fixed point with a constant speed.
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February 12, 2018
Spirals are polar graphs of the form r = n O~
Archimedean spiral logarithmic spiral
r = aebθ
Sketch the graph of each.
r=θ
r=2θ
r=.5θ
r=-2θ
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Design a pretty graph!!
Homework
6
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February 12, 2018