anonymous
  • anonymous
3-3sinx-2cos^2x = 0 Find all solutions in the domain [-pi,pi]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Just change cos2x into cos^2x-sin^2x and solve quadratic equation
Mertsj
  • Mertsj
\[3-3\sin x-2(1-\sin ^2x)=0\]
anonymous
  • anonymous
I just need someone to check answers with I got \[-\pi/2, \pi/2, 2\pi/3, -2\pi/3\]

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Mertsj
  • Mertsj
\[3-3\sin x-2+2\sin ^2x=0\]
Mertsj
  • Mertsj
Not what I got.
anonymous
  • anonymous
wait I mean
anonymous
  • anonymous
\[-\pi/2 , \pi/2 , 5\pi/6, -5\pi/6 , -\pi/6, \pi/6\]
Mertsj
  • Mertsj
Not what I got.
anonymous
  • anonymous
What did you get?
anonymous
  • anonymous
Once I factored the quadratic I got (2sinx-1) (sinx-1)=0
Mertsj
  • Mertsj
\[\frac{\pi}{6}, \frac{5\pi}{6}, \frac{\pi}{2}\]
Mertsj
  • Mertsj
Yes. So sinx=1/2 or 1
anonymous
  • anonymous
The domain is [-pi,pi] though?
Mertsj
  • Mertsj
Which is the same thing as [0,2pi]
anonymous
  • anonymous
Wait I don't get how that's the same?
anonymous
  • anonymous
The domain is negative pi to pi? How is it 0 to 2pi?
Mertsj
  • Mertsj
That means give all the solutions between - pi and pi . -pi to 0 would include quadrants 3 and 4. 0 to pi would include quadrants 1 and 2
anonymous
  • anonymous
But -pi/2 and -5pi/6 is between them?
Mertsj
  • Mertsj
The sin of -pi/2 is -1 The sin of -5pi/6 is -1/2
Mertsj
  • Mertsj
So those cannot be solutions.
Mertsj
  • Mertsj
And besides -pi/2 is the same as 3pi/2
Mertsj
  • Mertsj
And -5pi/5 is the same as 7pi/6
Mertsj
  • Mertsj
-5pi/6. Sorry for the typo
anonymous
  • anonymous
sin of -1 is 3pi/2 though
Mertsj
  • Mertsj
Do you mean that the sin of 3pi/2 is -1?
anonymous
  • anonymous
yeah, you said "The sin of -pi/2 is -1"
anonymous
  • anonymous
How can they both be?
Mertsj
  • Mertsj
And that is correct because the sin of -pi/2 is the same as the sin of 3pi/2
Mertsj
  • Mertsj
Let me draw you a picture.
Mertsj
  • Mertsj
|dw:1332469727207:dw|
anonymous
  • anonymous
Ok , I understand what you mean now. Thanks for clearing that up for me ! Guess I didn't get a 100 on my precal test :( Thanks so much Mertsj
Mertsj
  • Mertsj
Yw

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