Christos
WHERE IS MY MISTAKE?!?!?
Problem: Given that sinƟ = 2/3 and Π/2 < Ɵ < Π find the exact value of cosƟ
My solution:
cos^2(Ɵ) + sin^2(Ɵ) = 1
sin^2(Ɵ) = 1 - cos^2(Ɵ)
4/9=1- cos^2(Ɵ)
-5/9 = -cos^2(Ɵ)
5/9 = cos^2(Ɵ)
cos(Ɵ) = -sqrt(5/9)
Where is my mistake till now?
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anonymous
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for one thing, the square root of 9 is 3
anonymous
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so if you were typing in an answer, it probably wanted it to look like
\[\cos(\theta)=-\frac{\sqrt{5}}{3}\]
anonymous
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other than that, it is all correct
Christos
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@satellite73 So I didnt make any mistakes at all?
geerky42
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No.
Christos
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@satellite73 confirm to me please if all of my steps above were correct, and even if they had a mistake which line?
babycry
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just draw a triangle and with 0 = 2 and h = 3.. then find a then do a/h to get cos theta
Grazes
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|dw:1362625931832:dw|
anonymous
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there is no mistake, although you should have
\[\pm\sqrt{1-\left(\frac{2}{3}\right)^2}=\cos(\theta)\]
Christos
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I should have used another fundamental identity?
anonymous
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or if you write
\[\frac{5}{9}=\cos^2(\theta)\] then
\[\pm\frac{\sqrt{5}}{3}=\cos(\theta)\] the reason you know it is negative is because you are in quadrant 2
Christos
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got it its the same just modified, meeh
anonymous
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it is right, everything you did is right
Christos
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I know
why its negative yea
Christos
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problem is that My solution is different from the one on the book
anonymous
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so there is no mistake here, although you should have a 3 in the denominator, rather than the square root of 9
anonymous
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what did the book get?
Christos
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They the solutions might be equal but, I sill found a different solution
Christos
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5/9
anonymous
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a different solution, or a different method
Christos
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yea right..
anonymous
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nothing wrong with your method
answer is \(-\frac{\sqrt{5}}{3}\) for sure
Christos
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Books solution: 5/9
anonymous
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no that is \(\cos^2(\theta)\)
anonymous
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or else the book made a mistake
it happens
in any case you are right for sure, so don't fret about it
Christos
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what do you mean "no that is cos2(θ)" ?
anonymous
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\[\cos(\theta)=-\frac{\sqrt{5}}{3}\]
\[\cos^2(\theta)=\frac{5}{9}\]
Christos
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hmmmmm
Christos
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Is there any other method to approche the situation, like another identity to use for the specidif prob
Christos
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I AM SORRY the answer in my book was: -sqrt(5)/3 !!!!!
babycry
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|dw:1362626751880:dw|
Christos
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So my final outcome is - sqrt(5)/sqrt3 HOW DO I PROCEED?
Christos
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@satellite73
Christos
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@Hero
Christos
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@Mertsj
Christos
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SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE