## Babynini one year ago Let x =2sin(theta), -pi/2< theta<pi/2 Simplify the expression x/(sqroot(4-x^2)

1. Babynini

$\frac{ x }{ \sqrt{4-x^2} }$

2. Babynini

$\frac{ 2\sin(\theta) }{ \sqrt{4-(2\sin(\theta))^2} }$

3. Babynini

@UsukiDoll not sure where to go with this one! $\frac{ 2\sin(\theta) }{ 2-2\sin(\theta) }$ ??

4. UsukiDoll

hmm try factoring the 2 out of the denominator

5. Babynini

er..how do I do this xP

6. Babynini

is it 2(1-sintheta) ?

7. Babynini

in the denominator of course.

8. UsukiDoll

$\frac{ 2\sin(\theta) }{ 2(1-\sin(\theta)) }$ then cancel the 2

9. Babynini

and we're left with (sin(theta))/(1-sin(theta))

10. UsukiDoll

and then it turns into a mess... geez...

11. Babynini

haha aii

12. UsukiDoll

I'm wondering if that's it... It's been a while. but I know that the domain is restricted counter clockwise 90 degrees to clockwise 90 degrees.

13. Babynini

what if we ^2 the whole thing?

14. UsukiDoll

wait...

15. Babynini

we can add 180 later.. right? to get it into the correct domain.

16. UsukiDoll

$\frac{ 2\sin(\theta) }{ \sqrt{4-(2\sin(\theta))^2} }$ $\frac{ 2\sin(\theta) }{ \sqrt{4-4\sin^2(\theta))} }$ $\[\frac{ 2\sin(\theta) }{ \sqrt{4(1-\sin^2(\theta))} }$\]

17. UsukiDoll

$\frac{ 2\sin(\theta) }{ \sqrt{4(1-\sin^2(\theta))} }$

18. UsukiDoll

$\cos^2x+\sin^2x=1$ $\cos^2x = 1-\sin^2x$ $\frac{ 2\sin(\theta) }{ \sqrt{4(\cos^2(\theta))} }$

19. UsukiDoll

$\frac{2\sin(\theta)}{2\cos(\theta)}$

20. zepdrix

$\Large\rm \sqrt{4-4\sin^2x}\ne 2-2\sin x$You silly billy Miriam -_-

21. UsukiDoll

I got tangent theta in return?!

22. UsukiDoll

I saw something weird when I saw that I mean can't we yank the 4 out and use a trig identity

23. Babynini

Woah how'd you get tangent out of there? because the sin and cos are the same here?

24. UsukiDoll

$\sqrt{4-4\sin^2x} \rightarrow \sqrt{4(1-\sin^2x)}$

25. UsukiDoll

$\sqrt{4\cos^2x} \rightarrow 2cosx$

26. UsukiDoll

$\frac{2sinx}{2cosx} \rightarrow \frac{sinx}{cosx} \rightarrow tanx$

27. Babynini

oou..I see!

28. UsukiDoll

you've skipped a step and that trickled down later on

29. UsukiDoll

$(2\sin(\theta))^2 \rightarrow (2\sin(\theta))(2\sin(\theta))$

30. UsukiDoll

$4\sin^2(\theta)$

31. UsukiDoll

you've neglected to take the 2sin(theta) to the second power... that's why everything became nonsense

32. Babynini

Sorry, my internets really bad. yeah I was jumping around too much without checking o.0

33. Babynini

Sowriee