1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Having trouble getting this trigonometry problem started

  1. Oct 5, 2006 #1
    The problem is

    Solve [tex]sin(2y)=cos(4y) for y, where \\0\leq y \leq 360[/tex]

    This one is tricky, I want to try to equate either sin to cos or cos to sin so I can work with only one trig function, but how? I don't see how to start this problem. I know that the period of sin2y is 720deg or 4pi, and the period of cos4y is 8pi or 1440deg.
    Last edited: Oct 5, 2006
  2. jcsd
  3. Oct 5, 2006 #2


    User Avatar

    I'd start it by expanding Cos4y to (Cos2y)^2 - (Sin2y)^2.
    Sin2y = (Cos2y)^2 - (Sin2y)^2
    Sin2y= 1 - (Sin2y)^2 - (Sin2y)^2
    2(Sin2y)^2 + Sin2y - 1 = 0

    I'd probably use the Binomial theorem to solve the equasion from here. (EDIT - This can be factorised for a solution)
  4. Oct 6, 2006 #3
    Thanks alot acm, I appreciate it. :wink:

    Could someone tell me the rule though? Cos4y definitely does expand out to (Cos2y)^2 - (Sin2y)^2, but how?

    I would guess that Cos9y = (Cos3y)^2-(Sin3y)^2, but it doesn't...

    I just want something that I can write down in my notes so that I can use it in the future. Thanks. Or if someone could refer me to a website that would be perfect.
    Last edited: Oct 6, 2006
  5. Oct 6, 2006 #4


    User Avatar

  6. Oct 6, 2006 #5
    Ahhh thats right, I glanced over that handy identity, but should have put more effort into remembering it. Thanks!
  7. Oct 6, 2006 #6
    Thats actually neater then it looks :) I played around with it for a bit and realized that Cos(4x) = Cos(2x+2x) = cos(2x)cos(2x)-sin(2x)sin(2x)=(cos(2x))^2-(sin(2x))^2 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook