1. (0, 1 ) (1,0)  (r,0) (0,r) Circle of radius r

2. (0,1) (1,0)  (r,0) (0,r) (cos ,sin  ) 1

3. (0,1) (1,0)  (r,0) (0,r) (cos ,sin  ) 1

4. (0, 1 ) (1,0)  (r,0) (0,r) (cos ,sin  ) 1 (x, y) = (?,?) r

5. (0, 1 ) (1,0)  (r,0) (0,r) cos  sin  1 y x r (x, y) = (?,?)

6. (0, 1 ) (1,0)  (r,0) (0,r) cos  sin  1 y x r These are similar triangles, so the ratio of the sides are equal. (x, y) = (?,?)

7. (1,0)  cos  sin  1 y x r These are similar triangles, so the ratio of the sides are equal. (x, y) = (?,?) cos  1 

8.  sin  1 y x r These are similar triangles, so the ratio of the sides are equal.  vertical sides hypotenuses y = sin  r 1 so y = r sin 

9.  cos  sin  1 y x r These are similar triangles, so the ratio of the sides are equal.  vertical sides hypotenuses y = sin  r 1 so y = r sin  horizontal sides hypotenuses x = cos  r 1 so x = r cos 

10. (0, 1 ) (1,0)  (r,0) (0,r) (cos ,sin  ) 1 (x, y) = (r cos , r sin  )

11. (0, 1 )  (r,0) (0,r) (x, y) = (r cos , r sin  ) r cos  r sin 

12.  (r,0) (0,r) r cos  r sin  r

13.  (r,0) (0,r) r cos  r sin  r ? ?

14.  (r,0) (0,r) r cos  r sin  r ? ?

15.  (r,0) (0,r) r cos  r sin  r ? ?  r cos  r sin  r  ? ? r

16.  r cos  r sin  r  ? = h ? = y r These are similar triangles, so the ratio of the sides are equal.

17.  r cos  r sin  r  ? = h ? = y r These are similar triangles, so the ratio of the sides are equal. vertical sides horizontal sides y = r sin  r r cos  = tan  so y = r tan 

18.  r cos  r sin  r  ? = h ? = y r These are similar triangles, so the ratio of the sides are equal. vertical sides horizontal sides y = r sin  r r cos  = tan  so y = r tan  h = r r r cos  = 1 cos  = sec  so h = r sec  hypotenuses horizontal sides

19.  r cos  r sin  r  r sec  r tan  r

20.  (r,0) (0,r) r cos  r sin  r sec  r tan 

21.  (r,0) (0,r) r cos  r sin  r sec  r tan  Likewise: ? ?

22.  (r,0) (0,r) r cos  r sin  r sec  r tan  Likewise: r tan  r csc 

23.  = 45 o (2,0) (0,2) r = 2 (x, y) = Example:

24.  = 45 o (2,0) (0,2) r = 2 (x, y) = (r cos , r sin  ) =

25.  = 45 o (2,0) (0,2) r = 2 (x, y) = (r cos , r sin  ) = (2 cos 45 o,2 sin 45 o ) = ( (2)(  2/2),(2)(  2/2) ) = (  2,  2)

26.  = 120 o (4,0) (0,4) (x, y) = ? Example:

27.  = 120 o (4,0) (0,4) (x, y) = (r cos , r sin  ) =  r = 60 o

28.  = 120 o (4,0) (0,4) (x, y) = (r cos , r sin  ) = ( (4)( - 1/2), (4)(  3/2) ) ( - 2, 2  3)  r = 60 o

29.  = 210 o (3,0) (0,3) (x, y) = ? Example:

30. (3,0) (0,3) (x, y) = ?  r = 30 o Example:  = 210 o

31. (3,0) (0,3) (x, y) = (r cos , r sin  ) = (3(-cos 30 o ), 3(-sin 30 o )) = (-3  3 / 2, - 3/ 2 )  r = 30 o Example:  = 210 o (x, y) = ?

32. (3,0) (0,3) (x, y) = (-3  3 / 2, - 3/ 2 )  r = 30 o Example:  = 210 o