anonymous
  • anonymous
Solve: 1-sin(2πt)=0, for 0≤t≤2.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
we have: \[\Large \sin \left( {2\pi t} \right) = 1\]
Michele_Laino
  • Michele_Laino
now: sin x= 1 when: \[x = \frac{\pi }{2},2\pi + \frac{\pi }{2},4\pi + \frac{\pi }{2}...\]
Michele_Laino
  • Michele_Laino
for example, for the first solution, pi/2, we can write: \[2\pi t = \frac{\pi }{2}\] please solve for t

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More answers

anonymous
  • anonymous
t=2π?
triciaal
  • triciaal
no try again
anonymous
  • anonymous
t=π^2?
triciaal
  • triciaal
|dw:1437338469566:dw|
triciaal
  • triciaal
|dw:1437338527982:dw|
triciaal
  • triciaal
need the words?
triciaal
  • triciaal
are you here?
anonymous
  • anonymous
Oh... lol I am an idiot. xD
Nnesha
  • Nnesha
nah u r no8 :=)
anonymous
  • anonymous
Wait, so is 1/4 the answer?
zepdrix
  • zepdrix
\[\large\rm 2\pi t=\frac{\pi}{2}+2\pi k,\qquad k\in \mathbb{Z}\]Dividing by 2pi,\[\large\rm t=\frac{1}{4}+k,\qquad k\in \mathbb Z\]When k=0, yes you get t=1/4. That is one of your solutions. Think of other integers though. Which other integers for k will keep our t between 0 and 2?
anonymous
  • anonymous
Um... 3pie over 2?
freckles
  • freckles
integers. 3pi/2 is not an integer t=1/4+k where k is an integer are your candidates for solutions in the interval [0,2] notice for k=0 you have t=1/4 what happens if you let k=1?
anonymous
  • anonymous
So... 0 and 2?
freckles
  • freckles
so we want to find t in [0,2] such that \[0 \le t \le 2 \\ 0 \le \frac{1}{4}+k \le 2 \text{ from here you decide what \to \choose for } k \\ 0-\frac{1}{4} \le k \le 2-\frac{1}{4} \\ \text{ I subtracted } \frac{1}{4} \text{ on both sides } \\ \frac{-1}{4} \le k \le \frac{7}{4}\] what are the only integers in that inequality ?
anonymous
  • anonymous
0 and 2?
freckles
  • freckles
do you mean 0 and 1?
freckles
  • freckles
7/4 is less than 2 so 2 can't be included in that inequality above
anonymous
  • anonymous
Oh i see.
freckles
  • freckles
|dw:1437428007076:dw| only integers between -1/4 and 7/4 is 0 and 1
freckles
  • freckles
so these are the integers that @zepdrix was referring to
freckles
  • freckles
he already entered in 0 for k to get one solution for t now you just have to enter in 1 for k to get the other solution for t
freckles
  • freckles
\[t=\frac{1}{4}+k \\ \text{ when } k=0 \text{ we have } t=\frac{1}{4}+0=\frac{1}{4} \\ \text{ when } k=1 \text{ we have } t=?\]
freckles
  • freckles
I'm just asking you to replace k with 1
freckles
  • freckles
t=1/4+1=?
anonymous
  • anonymous
5/4
freckles
  • freckles
yes t=1/4 or t=5/4 are the only solutions for t in the given interval
anonymous
  • anonymous
Wow. that was intense... lol
anonymous
  • anonymous
Thank you
freckles
  • freckles
np lol the word intense is intense by itself (to me anyways)
anonymous
  • anonymous
Haha. Yea it is huh? xD

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