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?

1. satellite73

for one thing, the square root of 9 is 3

2. satellite73

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

3. satellite73

other than that, it is all correct

4. Christos

@satellite73 So I didnt make any mistakes at all?

5. geerky42

No.

6. Christos

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

7. babycry

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

8. Grazes

|dw:1362625931832:dw|

9. satellite73

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

10. Christos

I should have used another fundamental identity?

11. satellite73

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

12. Christos

got it its the same just modified, meeh

13. satellite73

it is right, everything you did is right

14. Christos

I know why its negative yea

15. Christos

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

16. satellite73

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

17. satellite73

what did the book get?

18. Christos

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

19. Christos

5/9

20. satellite73

a different solution, or a different method

21. Christos

yea right..

22. satellite73

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

23. Christos

Books solution: 5/9

24. satellite73

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

25. satellite73

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

26. Christos

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

27. satellite73

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

28. Christos

hmmmmm

29. Christos

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

30. Christos

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

31. babycry

|dw:1362626751880:dw|

32. Christos

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

33. Christos

@satellite73

34. Christos

@Hero

35. Christos

@Mertsj

36. Christos

SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE