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anonymous
 one year ago
Solve: 1sin(2πt)=0, for 0≤t≤2.
anonymous
 one year ago
Solve: 1sin(2πt)=0, for 0≤t≤2.

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have: \[\Large \sin \left( {2\pi t} \right) = 1\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now: sin x= 1 when: \[x = \frac{\pi }{2},2\pi + \frac{\pi }{2},4\pi + \frac{\pi }{2}...\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0for example, for the first solution, pi/2, we can write: \[2\pi t = \frac{\pi }{2}\] please solve for t

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437338469566:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437338527982:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh... lol I am an idiot. xD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait, so is 1/4 the answer?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm 2\pi t=\frac{\pi}{2}+2\pi k,\qquad k\in \mathbb{Z}\]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?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1integers. 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?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so 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 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.17/4 is less than 2 so 2 can't be included in that inequality above

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437428007076:dw only integers between 1/4 and 7/4 is 0 and 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so these are the integers that @zepdrix was referring to

freckles
 one year ago
Best ResponseYou've already chosen the best response.1he 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
 one year ago
Best ResponseYou've already chosen the best response.1\[t=\frac{1}{4}+k \\ \text{ when } k=0 \text{ we have } t=\frac{1}{4}+0=\frac{1}{4} \\ \text{ when } k=1 \text{ we have } t=?\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I'm just asking you to replace k with 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes t=1/4 or t=5/4 are the only solutions for t in the given interval

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow. that was intense... lol

freckles
 one year ago
Best ResponseYou've already chosen the best response.1np lol the word intense is intense by itself (to me anyways)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha. Yea it is huh? xD
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