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anonymous
 5 years ago
2 sin u cos u  2√2 sin u  cos u +√2=0. Find all solutions in the interval {0,360°)
any ideas where to start?
anonymous
 5 years ago
2 sin u cos u  2√2 sin u  cos u +√2=0. Find all solutions in the interval {0,360°) any ideas where to start?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0start by rewriting \[2sin(u)cos(u) =sin(2u)\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yikes. this one is a real pain. but it is doable i think. first replace sin(u) by x, cos(u) by y to rewrite as \[2xy2\sqrt{2}xy+\sqrt{2}=0\] \[2xy+\sqrt{2}=2\sqrt{2}x+y\] now square both sides. \[(2xy+\sqrt{2})^2=(2\sqrt{2}x+y)^2\] \[4x^2y^2+2\sqrt{2}xy+2=8x^2+4\sqrt{2}xy+y^2\] \[4x^2y^2+2=8x^2+y^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now since \[cos^2(u)=1sin^2(u)\] replace \[y^2\] by \[1x^2\] in the above equation. \[4x^2(1x^2)+2=8x^2+(1x^2)\] \[4x^24x^4=7x^2+1\] which is a quadratic equation in \[x^2\] so set = 0 and solve \[4x^43x^21=0\] \[(4x^2+1)(x^21)=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops i made a mistake. it is \[4x^4+3x^21=0\] \[(4x^21)(x^2+1)=0\] \[x^2+1=0\]has not solutions \[4x^21=0\] \[4x^2=1\] \[x^2=\frac{1}{4}\] \[x=\pm\frac{1}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[sin(x)=\frac{1}{2}\] \[x=30\] or \[x=150\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[sin(u)=\frac{1}{2}\] \[u=210\] \[u=330\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and now, (believe it or not we are not done) you have to check the answers because one step was to square both sides, so it is possible that one of the solutions was introduced during the squaring. i will let you do that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this was so long it makes me think that there is a snappier way to do it. if there is let me know.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i made a typo right in the beginning but it does not change the answer. in the second line \[(2xy+\sqrt{2})^2=4x^2y^2+4\sqrt{2}xy+2\] thats is why you can subtract the \[4\sqrt{2}xy\] from both sides.
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