SOLUTION: sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�)

Question 867653: sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�)
Answer by Edwin McCravy(20062) (Show Source): You can put this solution on YOUR website!

sin�(1�)+sin�(2�)+���+sin�(88�)+sin�(89�) =

Put some terms in the middle:

sin�(1�)+sin�(2�)+���+sin�(44�)+sin�(45�)+sin�(46�)+���+sin�(88�)+sin�(89�)

sin�(1�)+sin�(2�)+���+sin�(44�)+sin�(45�)+sin�(90�-44�)+���+sin�(90�-2�)+sin�(90�-1�)

Use the fact that sin(90�-q) = cos(q) 

sin�(1�)+sin�(2�)+���+sin�(44�)+sin�(45�)+cos�(44�)+���+cos�(2�)+cos�(1�) =

Rearrange the terms putting the 

1st and 89th terms together,

2nd and 88th terms together,

���

44th and 46th terms together: 

[sin�(1�)+cos�(1�)]+[sin�(2�)+cos�(2�)]+���+[sin�(44�)+cos�(44�)]+sin�(45�) =

Use the fact that sin�(q)+cos�(q) = 1

1 + 1 + ��� + 1 + sin�(45�), where there are 44 1's.

44 + sin�(45�) =

44 +  =

44 +  = 

44 +  =

44.5 

Edwin

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SOLUTION: sin�(1�)+sin�(2�)+���+sin�(88�)+sin�(89�)

SOLUTION: sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�)