anonymous
  • anonymous
Solve each of the following. Please give both the general solution and the specific solutions in the given interval. You may copy this page and put it into a word document then you can type or write directly on this sheet and attach to assignment 0.07.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
http://learn.flvs.net/webdav/educator_calculus_v8/module00/0_07a.htm
anonymous
  • anonymous
@John_ES
John_ES
  • John_ES
For the first question, \[\sin2\theta=-\frac{\sqrt{3}}{2}\]\[\Rightarrow 2\theta_1=\frac{4\pi}{3}\Rightarrow \theta_1=2\pi/3+2\pi k\]\[\Rightarrow 2\theta_2=\frac{5\pi}{3}\Rightarrow \theta_2=5\pi/6+2\pi k\]

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John_ES
  • John_ES
For the second question, \[2\sin^2x=2+\cos x\Rightarrow 2(1-\cos^2x)=2+\cos x\Rightarrow\]\[0=\cos x(2\cos x+1)\] We have, \[\cos x=0\Rightarrow x=\frac{\pi}{2}\]\[2\cos x+1=0\Rightarrow x=2\pi/3\]
anonymous
  • anonymous
But how do you know if its the general solution or the specific
John_ES
  • John_ES
You can only obtain a specific solution, because there is a limited range in the problem. So I must correct my first answer in the first problem, k must be zero there, because there are only these two solutions. In the second question the range specified is shorter, but again, is a specific solution.
anonymous
  • anonymous
How would we do the third one? tan(3x)(tanx-1)=0
anonymous
  • anonymous
I don't understand how to work these out.
John_ES
  • John_ES
This is a product of two factor equal to zero, so \[\tan(3x)=0\] gives you a solution. In this case, in order to get zero in the tangent, the argument must be zero, so, \[3x=0\Rightarrow x=0+2\pi k\] For the other solution we have, \[\tan x-1=0\Rightarrow \tan x=1\] In order to get 1 in the tangent, x must be, \[x_1=\pi/4+2\pi k\] But, there is another angle whose tangent is 1, in the third quadrant, \[x_2=5\pi/4+2\pi k\] These two solutions can be put together in one, \[x=\pi/4+\pi k\]
anonymous
  • anonymous
Awesome!!!!! Your great. Thanks for doing it step by step so I know what I'm actually doing. I hate when people just give you the answer. I like to learn how to do it
John_ES
  • John_ES
No problem ;)

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