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BloomLocke367
 one year ago
Solve this in interval form, from 0 to 2pi. Round to the nearest hundredth.
\(3sin2\theta=1.5\)
BloomLocke367
 one year ago
Solve this in interval form, from 0 to 2pi. Round to the nearest hundredth. \(3sin2\theta=1.5\)

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BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1@mathmate @pooja195

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1@dan815 Will you come help?

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 Can you please help?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2as a start, divide 3 both sides

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[3\sin(2\theta) = 1.5 \implies \sin(2\theta) = \frac{1.5}{3} =\frac{1}{2} \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\sin(2\theta) = \frac{1}{2} \implies 2\theta = \sin^{1}\left(\frac{1}{2}\right)\] look up unit circle

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1I have the unit circle

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1what am I looking for?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2see for what angles the sin value is \(\frac{1}{2}\)

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1sin is the yvalue, right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1432912910233:dw

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1so, 7pi/6 and 11pi/6

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1and I just round that to the nearest hundredth and I'll have my answer?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, \[2\theta = \frac{7\pi}{6}+2k\pi,~ ~\frac{11\pi}{6}+2k\pi\] that means \[\theta = \frac{7\pi}{12}+k\pi,~ ~\frac{11\pi}{12}+k\pi\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2but you want solutions in the interval 0 to 2pi, right ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2plugin k = 0, 1, 2 etc till you hit 2pi

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\theta = \frac{7\pi}{12}+k\pi,~ ~\frac{11\pi}{12}+k\pi\] plugin \(k=0\) and get \[\theta = \frac{7\pi}{12},~ ~\frac{11\pi}{12}\] plugin \(k=1\) and get \[\theta = \frac{7\pi}{12}+\pi,~ ~\frac{11\pi}{12}+\pi\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2because any integer value of \(k\) gives an angle that is a solution to the given equation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2there are infinitely many solutions as there are infinitely many integers your question is about finding the solutions in the interval 0 to 2pi

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1and you plug in k=2, and get \(\large\frac{7\pi}{12}+2\pi,~\frac{11\pi}{12}+2\pi\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes clearly thats more than \(2\pi\), so we may stop now.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2k=0 and k=1 are enough

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2find the corresponding \(\theta\) values as you can see there are exactly four solutions in the interval 0 to 2pi

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1okay, and I just round it?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2the question asks you to round it so yeah

BloomLocke367
 one year ago
Best ResponseYou've already chosen the best response.1so, 1.83, 2.88, 4.97, and 6.02

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Looks good, you may double check with wolfram http://www.wolframalpha.com/input/?i=solve%203sin(2%5Ctheta)%3D1.5%2C%200%3C%5Ctheta%3C2pi&t=crmtb01
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