1. 4.2 The Unit Circle!
Whoa wait a sec, where does all that stuff come from?

2. Let's go on a unit circle adventure and find out!
Since our special right triangles (or commonly used triangles are and , let's split our circle into increments of 30 (12ths of the circle) and 45 (eights of the circle).

3. Convert degrees to radians

4. fourths of full circle, halfs of half circle
eights of full circle, fourths of half circle
think 45/360 = 1/8
think 90/360 = 1/4

5. twelfths of full circle, sixths of half circle
think 30/360 = 1/12

6. Mind Blown

7. Review! SOHCAHTOA Special Right Triangles
What if the hypotenuse was 1?
SOHCAHTOA
Special Right Triangles

9. Let's talk special right triangles
With a hypotenuse of
1, find the missing side
lengths using the Pyth. thm.
Triangle l 45 1
x 2 45 x 45 x
Find sin(45)=
cos(45)=
tan(45)=

10. Let's talk special right triangles
With a hypotenuse of 1, find the missing side lengths using the Pythagorean thm.
hint: think of an equilateral triangle
Triangle 1 2x 60 60 x 30 30
x 3
Find sin(30)=
cos(30)=
tan(30)=
Find sin(60)=
cos(60)=
tan(60)=

11. Now we can find the coordinates of each point on the circle
Remember the hypotenuse is 1! 30 60 45 x y 1 30 60
cos(45) = x/1
x = cos(45)
x =
sin(45) = y/1
y = sin(45)
y =
cos(30) = x/1
x = cos(30)
x =
sin(30) = y/1
y = sin(30)
y =

12. (mind blown) 2