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Solve the equation sin x cos x = `sqrt 3 / 4`

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atrinity | Honors

Posted April 17, 2013 at 5:44 PM via web

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Solve the equation sin x cos x = `sqrt 3 / 4`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 17, 2013 at 6:16 PM (Answer #1)

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The equation `sin x cos x = sqrt 3 / 4` has to be solved.

`sin x cos x = sqrt 3 / 4`

=> `2*sin x*cos x = sqrt 3/2`

=> `sin (2x) = sqrt 3/2`

=> 2x = 60 and 2x = 120

=> x = 30 and x = 60 degrees

The general solution of the equation is 30 + n*360 degrees and 60 + n*360 degrees.

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oldnick | Valedictorian

Posted April 18, 2013 at 1:40 AM (Answer #2)

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`sinxcosx= 1/2(sin(x+x)-sin(x-x))=1/2sin2x```

so:

`1/2sin2x=sqrt(3)/4i`   `sin2x=sqrt(3)/2`     `2x=pi/3`   `2x=2/3pi`

 

`x=pi(1/3+2k)`   `x=2pi(1/3+k)`

 

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