Geometry: An Interactive Journey to Mastery

Lesson 18: What Is the Sine of 1°?

6. 
   

   Show that tan 2 x (^) 1tan2tan 2 xx.

   
   


7. 
   

   Show that tan xy 1tantantan xyxytan.

   
   


8. 
   

   Consider a triangle with side lengths a, b, and c, as shown in
   Figure 18.4/HWm be the length of the median of the triangle
   to the side cͼ௘7KLVOLQHFRQQHFWVRQHYHUWH[RIWKHWULDQJOH
   to the midpoint of the side of length c௘ͽ
   8VHWKHODZRIFRVLQHVͼ௘WZLFH²HDFKWLPHWRWKHDQJOHPDUNHGx௘ͽWRHVWDEOLVKHV$SROORQLXV¶VHTXDWLRQ
   ab^22  c 22 2.m^2

   
   


9. 
   

   The diagram in Figure 18.5 shows that tan©¹ ̈ ̧§·21cosxx (^) sin x. How?
   It also shows that tan©¹§· ̈ ̧2sinxx 1cos x. How?

   
   


10. 
    

    Prove that sinxy sin 2 sin©¹©¹ ̈ ̧ ̈ ̧§·§·xy 22 cos xy.

    
    

a

b

c

m

x

Figure 18.4

1

1

x

2 x

2 x

Figure 18.5