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

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

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

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

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

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

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

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

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

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

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

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

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

satellite73
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0what do you mean "no that is cos2(θ)" ?

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

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

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

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