Post a New Question

Trigonometry - Proofs

posted by .

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.

  • Trigonometry - Proofs -

    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

    Gotta think some more. Back later. See what you can figure out.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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(a-b) = sin(a)cos(b) - cos(a)sin(b) …
  2. algebra

    Can someone please help me do this problem?
  3. 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 …
  4. 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; …
  5. Trigonometry

    Does anyone have a good website that shows the proofs for these equations?
  6. 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 …
  7. 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/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove that …
  8. Pre-Calculus

    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 t-sin^4 t=1-2sin^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 …
  9. 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 …
  10. math


More Similar Questions

Post a New Question