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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.2
for one thing, the square root of 9 is 3
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
so if you were typing in an answer, it probably wanted it to look like \[\cos(\theta)=\frac{\sqrt{5}}{3}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
other than that, it is all correct
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
@satellite73 So I didnt make any mistakes at all?
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
@satellite73 confirm to me please if all of my steps above were correct, and even if they had a mistake which line?
 one year ago

babycryBest ResponseYou've already chosen the best response.0
just draw a triangle and with 0 = 2 and h = 3.. then find a then do a/h to get cos theta
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
there is no mistake, although you should have \[\pm\sqrt{1\left(\frac{2}{3}\right)^2}=\cos(\theta)\]
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
I should have used another fundamental identity?
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
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
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
got it its the same just modified, meeh
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
it is right, everything you did is right
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
I know why its negative yea
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
problem is that My solution is different from the one on the book
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
so there is no mistake here, although you should have a 3 in the denominator, rather than the square root of 9
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
what did the book get?
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
They the solutions might be equal but, I sill found a different solution
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
a different solution, or a different method
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
nothing wrong with your method answer is \(\frac{\sqrt{5}}{3}\) for sure
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
no that is \(\cos^2(\theta)\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
or else the book made a mistake it happens in any case you are right for sure, so don't fret about it
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
what do you mean "no that is cos2(θ)" ?
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
\[\cos(\theta)=\frac{\sqrt{5}}{3}\] \[\cos^2(\theta)=\frac{5}{9}\]
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
Is there any other method to approche the situation, like another identity to use for the specidif prob
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
I AM SORRY the answer in my book was: sqrt(5)/3 !!!!!
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
So my final outcome is  sqrt(5)/sqrt3 HOW DO I PROCEED?
 one year ago

ChristosBest ResponseYou've already chosen the best response.0
SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE
 one year ago
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