<p>Hey everyone. My teacher gave a pretty confusing problem today for homework. Then again, I'm not a strong math person so it'll probably be easy to a lot of you. If anyone can help, I'd greatly appreciate it! :)</p>
<p>Find all the solutions of the equation in the interval [0, 2 pi):</p>
<p>4cos^2 2x-1=0</p>
<p>HINT: THERE ARE 8 SOLUTIONS!</p>
<p>Thanks guys!
:)</p>
<p>is the 2x multiplied by the 4cos^2?</p>
<p>It's easy, man.</p>
<p>Just throw that mother in your calculator...</p>
<p>y=4cos(2x-1)^2</p>
<p>And you can write down every time it = 0 (crosses the x axis, but make sure that it's in terms of pi)</p>
<p>Or...</p>
<p>You can just set it equal to 0, as it is, and solve that mother. I think cos(x)^2 equals something funky.</p>
<p>I think it's the cos squared of (2x-1).</p>
<p>4cos^2(2x-1) = 0
Pull the coefficient 4 out and use the power reducing identity on the cos which is
cos^2 x = [1 + cos(2x)]/2
When you use that identity you get
4*([1+cos(4x-2)]/2)
When you multiply you get
2 + 2cos(4x-2) = 0
Subtract 2 from both sides
2cos(4x-2) = -2
Divide by 2
cos(4x-2) = -1
From there just find all the values of x that makes the entire thing equal -1. Somebody please let me know if I made a mistake, since I've been out of trigonometry for a while now.</p>
<p>Thank you guys! :)</p>
<p>oh, you're very welcome</p>
<p>hey, how did martha get to say your welcome?
lol!</p>
<p>That's what I'm wondering. I think she was <em>trying</em> to be sarcastic.</p>
<p>Haha........</p>
<p>...........lol!</p>
<p>this poor thread....it died</p>
<p>is there any reason for it not to have?</p>
<p>Wow, thats awesome, I did the same sort of thing for hw tonight (are you on block schedualing too)</p>
<p>aww...it died AGAIN</p>