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anonymous
 one year ago
Solve Trig Equation
\( tan \theta = \frac{2\sqrt{3}}{3} sin \theta \)
anonymous
 one year ago
Solve Trig Equation \( tan \theta = \frac{2\sqrt{3}}{3} sin \theta \)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need to get the solution sets

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0hint u can write tan(theta) as sin(theta)/cos(theta)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, first off we should note that we cannot have solutions that would make cosine equal to 0, as then we would have something undefined. So let me change tangent into sin/cos and do this: \[\frac{ \sin\theta }{ \cos\theta } = \frac{ 2\sqrt{3} }{ 3 }\sin\theta\] \[\sin\theta = \frac{ 2\sqrt{3} }{ 3 }\sin\theta\cos\theta\] \[\frac{ 2\sqrt{3} }{ 3 }\sin\theta\cos\theta  \sin\theta = 0\] Now factor and see if you solve from there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433617958179:dw

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0nw cancel sin(theta) from both sides of the equation

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0then u'll b left with 1/cos(theta) = 2/root(3) cross multiplying we get cos(theta) = root(3)/2 which is equal to cos(30) therefore theta = 30degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In general, you do not want to cancel sin(theta) from both sides of the equation, or divide by any variable expression for that manner. If you do this, you could potentially lose solutions.

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0cos(theta) = cos(30) = cos(330)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To show this, by inspection you can see that 0 would be a solution to this equation. Yet if you divide out sin(theta), you completely lose 0 as a solution in what would be remaining.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am stuck on factoring the last part

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\tan(0) = \frac{ 2\sqrt{3} }{ 3 }\sin(0)\] YOu get 0 = 0. You lose this solution if you cancel out sin(theta) from both sides.

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0ok m posting a full solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0As for the factoring, where I have \[\frac{ 2\sqrt{3} }{ 3 }\sin\theta\cos\theta  \sin\theta = 0\] you can factor out sin(theta) \[\sin \theta(\frac{ 2\sqrt{3} }{ 3 }\cos\theta 1) = 0\] This gives two possibilities. \[\sin\theta = 0\] or \[\frac{ 2\sqrt{3} }{ 3 }\cos\theta 1 = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433618602641:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You cannot divide by sin(theta). In general, you cannot divide by variable expression. Notice that I had one of my potential results when I factored as sin(theta) = 0. You completely lose this solution if you divide out sin(theta), you are not allowed to do this @Nixy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where does the 1 come from? Is it because cos sin = cos  1 sin ???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0As a small example of why the 1, consider 2x2. I can factor a 2 out of this expression and get 2(x1). When you factor a number out of itself, it leaves behind a 1. You can also distribute to check this result if you wish.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But from above, I have solutions that will come from \[\sin\theta = 0\] and \[\frac{ 2\sqrt{3} }{ 3 }\cos\theta  1 = 0\]

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.0√3 tan x = 2 sin x √3 tan x  2 sin x = 0 sin x ( √3/cos x  2 ) = 0 => sin x = 0 or √3 / cos x  2 = 0 when sin x = 0 x = 2kpi where k= 0,1,2,3......... when √3 / cos x  2 = 0 => cos x = √3/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I got it. Thanks to you all

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep I got it. My solutions were 0, pi, 5pi/6, 7pi/6 Thanks once again to you all.
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