5/3/12 How do we find the area of sectors and other parts of a circle?

How do we find the area of sectors and other parts of a circle?

Sector of a circle
- a sector of a circle is the region between the radii and the arc of a sector
To find the area of a sector : # of degrees /360 x (pi) r^2
Ex:

Segment of a circle 
- a segment of a circle is the region between a chord and arc of circle
To find the area of the segment of a circle : # of degrees/360 x  (pi)r^ - 1/2bh
Ex:

Annulus 
- an annulus is the region between two concentric circles
To find the area of the annulus : (pi)R^2- (pi)r1

Ex:

Practice question : If radius 1 is 12 and radius 2 is 6, What is the area of the annulus?

                                                           Citations
- Problem solving , http://www.p12.nysed.gov/ciai/mst/math/sampletasks/Math6Sample.htm
- Chord and segment of a circle, http://www.winpossible.com/lessons/Chord_and_Segment_Of_A_Circle.aspx, 2011
- Annulus calculator , http://www.calculatorsoup.com/calculators/geometry-plane/annulus.php

5/1/12 How do we use secant , chord and tangents in circles? ?

How do we use Secants, Chords and Tangents in circles?

Secant
- a line that cuts through or divides a curve into two or more parts
Ex:

Chord
- a straight line thats joins the ends of an arc
Ex :

Tangent
-  straight line or plane that touches a curve or curved surface at a point
Ex:

Practice Question : What does the line TL image below represent?

                                                                       Citations 
- Chord , Wolfram MathWorld , http://mathworld.wolfram.com/Chord.html , 2012

- http://www.google.com/imgres?q=secant&start=173&um=1&hl=en&sa=N&biw=1280&bih=861&addh=36&tbm=isch&tbnid=Lo2YH7az3PTd1M:&imgrefurl=https://internal.shenton.wa.edu.au/maths/WestOne3CMAS/content/004_functions/media/glossary.html&docid=r1W_zcdlQ_KVDM&imgurl=https://internal.shenton.wa.edu.au/maths/WestOne3CMAS/content/004_functions/media/images/glossary_secant.gif&w=290&h=250&ei=QcymT8myJqGJ6QGyiaCdBA&zoom=1&iact=hc&vpx=606&vpy=126&dur=282&hovh=179&hovw=216&tx=126&ty=147&sig=100793830460579110965&page=8&tbnh=152&tbnw=195&ndsp=25&ved=1t:429,r:7,s:173,i:194

- Chapter 9: Chords and Arcs, http://whites-geometry-wiki.wikispaces.com/PETO626
- Geometry : Circles , http://www.sparknotes.com/math/geometry1/circles/section3.rhtml , 2012

How do we review transformations?

Isometry

- length is preserved

- sides are congruents ( like their reflecting)

Ex:                         

              

Direct isometry 

- orientation is preserved( stays the same)

-  The order of the lettering in the figure and the images are the same 

- either clockwise becomes counter clockwise or counter clockwise becomes clockwise 

- every translation and rotation is a direct isometry

Ex: 

Opposite isometry

- orientation isn't preserved (changes)

-  the order of the lettering is reversed

- every reflection and glide reflection is an opposite isometry 

 Ex:

Same orientation :

 rorgin (x,y) -> (-x,-y)              

 R90 (x,y) -> (-y,x)

 R180 ( x,y)-> (-x,-y)

 R270 ( x,y) -> ( y,-x)

Reversed orientation:

 r- x-axis (x,y) -> ( x,-y)

 r-y-axis (x,y) ->(-x,y)

ry = x (x,y) -> ( y,x)

ry = -x (x,y) -> (-y,-x)

Practice question : What is the difference between a direct and opposite isometry?

                                                      Citations 

- http://zsolania.blogspot.com/

- Haskell , Kenn, Functional Lens , http://www.kennknowles.com/blog/2007/12/03/calculating-the-reflect-rotate-translate-normal-form-for-an-isometry-of-the-plane-in-haskell-and-verifying-it-with-quickcheck/