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

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- anonymous

for one thing, the square root of 9 is 3

- anonymous

so if you were typing in an answer, it probably wanted it to look like
\[\cos(\theta)=-\frac{\sqrt{5}}{3}\]

- anonymous

other than that, it is all correct

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## More answers

- Christos

@satellite73 So I didnt make any mistakes at all?

- geerky42

No.

- Christos

@satellite73 confirm to me please if all of my steps above were correct, and even if they had a mistake which line?

- anonymous

just draw a triangle and with 0 = 2 and h = 3.. then find a then do a/h to get cos theta

- anonymous

|dw:1362625931832:dw|

- anonymous

there is no mistake, although you should have
\[\pm\sqrt{1-\left(\frac{2}{3}\right)^2}=\cos(\theta)\]

- Christos

I should have used another fundamental identity?

- anonymous

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

got it its the same just modified, meeh

- anonymous

it is right, everything you did is right

- Christos

I know
why its negative yea

- Christos

problem is that My solution is different from the one on the book

- anonymous

so there is no mistake here, although you should have a 3 in the denominator, rather than the square root of 9

- anonymous

what did the book get?

- Christos

They the solutions might be equal but, I sill found a different solution

- Christos

5/9

- anonymous

a different solution, or a different method

- Christos

yea right..

- anonymous

nothing wrong with your method
answer is \(-\frac{\sqrt{5}}{3}\) for sure

- Christos

Books solution: 5/9

- anonymous

no that is \(\cos^2(\theta)\)

- anonymous

or else the book made a mistake
it happens
in any case you are right for sure, so don't fret about it

- Christos

what do you mean "no that is cos2(θ)" ?

- anonymous

\[\cos(\theta)=-\frac{\sqrt{5}}{3}\]
\[\cos^2(\theta)=\frac{5}{9}\]

- Christos

hmmmmm

- Christos

Is there any other method to approche the situation, like another identity to use for the specidif prob

- Christos

I AM SORRY the answer in my book was: -sqrt(5)/3 !!!!!

- anonymous

|dw:1362626751880:dw|

- Christos

So my final outcome is - sqrt(5)/sqrt3 HOW DO I PROCEED?

- Christos

@satellite73

- Christos

@Hero

- Christos

@Mertsj

- Christos

SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE

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