Homework Help

Which is the value of the sum cos177+cos176+...cos4+cos3 ?

user profile pic

sirserie | Student, Grade 10 | eNoter

Posted August 17, 2010 at 11:52 PM via web

dislike 1 like

Which is the value of the sum cos177+cos176+...cos4+cos3 ?

Tagged with math

4 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted August 17, 2010 at 11:55 PM (Answer #1)

dislike 0 like

We'll apply the formula

cos(180-k)=-cos k

-cos 3 = cos (180-3)=cos 177

-cos 4 = cos (180-4)=cos 176

.......................................................

We'll re-write the sum:

S = - cos 3 - cos 4 -.....- cos 89 + cos 90 + cos 89 + ....+cos4 + cos3

We'll eliminate like terms:

S = 0

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted August 18, 2010 at 12:08 AM (Answer #2)

dislike 0 like

S = cos177 + cos176 + .....+ cos4 + cos3

Let us rewrite:

S = cos(180-3) + cos(180 -4) + ----+ cos4 + cos3

But, we know that :

cos(180 -a) = - cosa

==> S = -cos3 - cos4 + ...+ cos4 + cos3

By eliminating similar,

==> S = 0

 

user profile pic

neela | High School Teacher | Valedictorian

Posted August 18, 2010 at 12:51 AM (Answer #3)

dislike 0 like

Cos177+cos176+ cos 175 + .. cos91+cos90+co89+.. ...cos4 +cos3 . To find the sum.

We know that cos (90+n) =  -cos(90-n),

So the given series is equal to Sum of {cos(90+n)+cos(90-n) + cos 90  for n = 1 ,2,3,....97.

= Sum of ( 0) +cos90 , for each n = 1.2,3...87.

= 0. as cos 90 = 0. 

 

user profile pic

jeyaram | Student , Undergraduate | Valedictorian

Posted August 18, 2010 at 6:55 PM (Answer #4)

dislike 0 like

cos177+cos176+...+cos4+cos3

=cos(180-3)+cos(180-4)+....+cos4+cos3

=(-cos3)+(-cos4)+.....+cos4+cos3

=0

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes