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Christos
 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?
Christos
 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?

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satellite73
 one year ago
Best ResponseYou've already chosen the best response.2for one thing, the square root of 9 is 3

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2so if you were typing in an answer, it probably wanted it to look like \[\cos(\theta)=\frac{\sqrt{5}}{3}\]

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2other than that, it is all correct

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

Christos
 one year ago
Best 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?

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2there is no mistake, although you should have \[\pm\sqrt{1\left(\frac{2}{3}\right)^2}=\cos(\theta)\]

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2or 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
 one year ago
Best ResponseYou've already chosen the best response.0got it its the same just modified, meeh

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2it is right, everything you did is right

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

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2so there is no mistake here, although you should have a 3 in the denominator, rather than the square root of 9

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2what did the book get?

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2a different solution, or a different method

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2nothing wrong with your method answer is \(\frac{\sqrt{5}}{3}\) for sure

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2no that is \(\cos^2(\theta)\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2or else the book made a mistake it happens in any case you are right for sure, so don't fret about it

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2\[\cos(\theta)=\frac{\sqrt{5}}{3}\] \[\cos^2(\theta)=\frac{5}{9}\]

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

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

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

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