Trigonometry  Proofs
posted by Sam .
Prove that the average of the numbers n sin (n degrees) (n = 2, 4, 6, ... 180) is cot (1 degree)
Hint: Express everything in terms of sin and cos. Can you rearrange the result into a form that allows you to use some of the identities you've learned?
How to start? I know I have to use trigonometric identities but where?
Thanks a lot.

sin0+180sin180 = 0sin0 + 180sin0
2sin2 + 178sin178 = 2sin2 + 178sin2 = 180sin2
...
88sin88 + 102sin102 = 180sin88
so, we have
180(sin0 + sin2 + sin4 + ... + sin88) + 90sin90
= 180(sin0+sin2+...+sin90)  90
That makes the average
2(sin0+sin2+...+sin90)1
Gotta think some more. Back later. See what you can figure out.
Respond to this Question
Similar Questions

tigonometry
expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by b and using that cos(b)= cos(b) sin(b)= sin(b) gives: sin(ab) = sin(a)cos(b)  cos(a)sin(b) … 
algebra
Can someone please help me do this problem? 
Mathematics  Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y … 
Trigonometry
Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; … 
Trigonometry
Does anyone have a good website that shows the proofs for these equations? 
Trigonometry
Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees … 
Trigonometry
1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places. 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1tanθ = sec^2θ+2tanθ/1tan^2θ 17.Prove that … 
PreCalculus
I don't understand,please be clear! Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 tsin^4 t=12sin^2 t 2. 1/cos s= csc^2 s  csc s cot s 3. (cos x/ sec x 1) (cos x/ tan^2x)=cot^2 x … 
math
Express each of the following in terms of another angle between 0 degrees and 180 degrees a. sin 50 degrees b. sin 150 degrees c. cos 45 degrees d. cos 120 degrees please explain to me how to answer this question you don't have to … 
math
PLEASE HELP ME WITH THIS TRIGONOMETRY QUESTION!!?