https://myfiles.st-agnes.org/Users/Students/lhoman/OSP.doc?uniq=bkn5nv

Laura Homan

Warm up (turned in):
write formula from geometry for...
     - length of an arc of a circle
     - length of the area of a sector of a circle
(answers green box on p. 779 of textbook)

- an angle is two rays
- the measure of an angle is negative when starting with the initial side and going counter-clockwise toward the terminal side (diagram shown on p. 776 of textbook)
- co-terminal means the angles share the same terminal side
- an angle can be found by adding or subtracting 360 degrees from another co-terminal angle.
- when converting degrees to radians or radians to degrees (p. 777) just think of it as dimensional analysis
    ex:      30 degrees  .          pi           =    pi  
                                    180 degrees          6

Handout:
use p. 777 to help understand

We got a handout in class, so ask about that. 

Warm up:

1. Cos 30= .866 or sq.root of 3 over 2

Sin 30= .500 or 1/2

2. Cos 60= .500 or 1/2

Sin 60= .866 or sq. root of 3 over 2

3. Cos 45= .707 or sq. root of 2 over 2

Sin 45= .707 or sq. root of 2 over 2.

The Unit Circle

For the 90-45-45 triangle, there are four main points you need to know: (a,b), (-a,b), (a,-b), and (-a,-b)

(a,b)= (s.r 2 over 2, s.r 2 over 2)

(-a,b)= (-s.r 2 over 2, s.r 2 over 2)

(a,-b)= (s.r 2 over 2, -s.r 2 over 2)

(-a,-b)= (-s.r 2 over 2, -s.r 2 over 2)

For the 90-30-30 triangle, there are 8 points. (going counter clockwise)

(s.r 3 over 2, 1/2)

(1/2, s.r 3 over 2)

(-1/2, s.r 3 over 2)

(-s.r 3 over 2, 1/2)

(-s.r 3 over 2, -1/2)

(-1/2, -s.r 3 over 2)

(1/2, -s.r 3 over 2)

(s.r 3 over 2, -1/2)

*****The first number in the ordered pairs are the cosines of the angle and the second number in the ordered pairs are the sines of the angle!!!!!

Point P= t

Point Q= pi-t

Point R= pi + t

Point S= 2pi - t