Christos Group Title 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

1. satellite73 Group Title

for one thing, the square root of 9 is 3

2. satellite73 Group Title

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

3. satellite73 Group Title

other than that, it is all correct

4. Christos Group Title

@satellite73 So I didnt make any mistakes at all?

5. geerky42 Group Title

No.

6. Christos Group Title

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

7. babycry Group Title

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

8. Grazes Group Title

|dw:1362625931832:dw|

9. satellite73 Group Title

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

10. Christos Group Title

I should have used another fundamental identity?

11. satellite73 Group Title

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 Group Title

got it its the same just modified, meeh

13. satellite73 Group Title

it is right, everything you did is right

14. Christos Group Title

I know why its negative yea

15. Christos Group Title

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

16. satellite73 Group Title

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

17. satellite73 Group Title

what did the book get?

18. Christos Group Title

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

19. Christos Group Title

5/9

20. satellite73 Group Title

a different solution, or a different method

21. Christos Group Title

yea right..

22. satellite73 Group Title

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

23. Christos Group Title

Books solution: 5/9

24. satellite73 Group Title

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

25. satellite73 Group Title

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 Group Title

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

27. satellite73 Group Title

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

28. Christos Group Title

hmmmmm

29. Christos Group Title

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

30. Christos Group Title

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

31. babycry Group Title

|dw:1362626751880:dw|

32. Christos Group Title

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

33. Christos Group Title

@satellite73

34. Christos Group Title

@Hero

35. Christos Group Title

@Mertsj

36. Christos Group Title

SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE