The value of
 sum from r equals 0 to 9 of sin squared open parentheses πr over 18 close parentheses space space i s space e q u a l space t o
left parenthesis A right parenthesis 9 over 2 space space space left parenthesis B right parenthesis 7 over 2 space space space left parenthesis C right parenthesis 5 space space space space space left parenthesis D right parenthesis 4

Asked by araima2001 | 4th Apr, 2017, 04:06: AM

Expert Answer:

begin mathsize 16px style begin inline style sum from straight r equals 0 to straight r equals 9 of end style space sin squared open parentheses πr over 18 close parentheses
equals space sin squared open parentheses 0 close parentheses plus space sin squared open parentheses fraction numerator pi cross times 1 over denominator 18 end fraction close parentheses plus space sin squared open parentheses fraction numerator pi cross times 2 over denominator 18 end fraction close parentheses plus space sin squared open parentheses fraction numerator pi cross times 3 over denominator 18 end fraction close parentheses plus........... plus space sin squared open parentheses fraction numerator pi cross times 9 over denominator 18 end fraction close parentheses
Now space we space will space convert space radian space angles space in space degrees comma
equals 0 plus space sin squared open parentheses 10 close parentheses plus space sin squared open parentheses 20 close parentheses plus space sin squared open parentheses 30 close parentheses plus space sin squared open parentheses 40 close parentheses plus space sin squared open parentheses 50 close parentheses plus space sin squared open parentheses 60 close parentheses plus space sin squared open parentheses 70 close parentheses plus space sin squared open parentheses 80 close parentheses plus space sin squared open parentheses 90 close parentheses
equals space open square brackets sin squared open parentheses 10 close parentheses plus sin squared open parentheses 80 close parentheses close square brackets plus space open square brackets sin squared open parentheses 20 close parentheses plus sin squared open parentheses 70 close parentheses close square brackets plus open square brackets sin squared open parentheses 30 close parentheses plus sin squared open parentheses 60 close parentheses close square brackets plus open parentheses sin squared open parentheses 40 close parentheses plus space sin squared open parentheses 50 close parentheses close parentheses plus sin squared open parentheses 90 close parentheses
Using space sin squared straight theta equals cos squared open parentheses 90 degree minus straight theta close parentheses space also space space sin squared straight theta plus cos squared straight theta equals 1
equals 1 plus 1 plus 1 plus 1 plus 1
equals 5
end style

Answered by Sneha shidid | 4th Apr, 2017, 01:55: PM