Babynini
  • Babynini
Let x =2sin(theta), -pi/2< theta
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Babynini
  • Babynini
\[\frac{ x }{ \sqrt{4-x^2} }\]
Babynini
  • Babynini
\[\frac{ 2\sin(\theta) }{ \sqrt{4-(2\sin(\theta))^2} }\]
Babynini
  • Babynini
@UsukiDoll not sure where to go with this one! \[\frac{ 2\sin(\theta) }{ 2-2\sin(\theta) }\] ??

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More answers

UsukiDoll
  • UsukiDoll
hmm try factoring the 2 out of the denominator
Babynini
  • Babynini
er..how do I do this xP
Babynini
  • Babynini
is it 2(1-sintheta) ?
Babynini
  • Babynini
in the denominator of course.
UsukiDoll
  • UsukiDoll
\[\frac{ 2\sin(\theta) }{ 2(1-\sin(\theta)) }\] then cancel the 2
Babynini
  • Babynini
and we're left with (sin(theta))/(1-sin(theta))
UsukiDoll
  • UsukiDoll
and then it turns into a mess... geez...
Babynini
  • Babynini
haha aii
UsukiDoll
  • 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.
Babynini
  • Babynini
what if we ^2 the whole thing?
UsukiDoll
  • UsukiDoll
wait...
Babynini
  • Babynini
we can add 180 later.. right? to get it into the correct domain.
UsukiDoll
  • UsukiDoll
\[\frac{ 2\sin(\theta) }{ \sqrt{4-(2\sin(\theta))^2} }\] \[\frac{ 2\sin(\theta) }{ \sqrt{4-4\sin^2(\theta))} }\] \[\[\frac{ 2\sin(\theta) }{ \sqrt{4(1-\sin^2(\theta))} }\]\]
UsukiDoll
  • UsukiDoll
\[\frac{ 2\sin(\theta) }{ \sqrt{4(1-\sin^2(\theta))} }\]
UsukiDoll
  • UsukiDoll
\[\cos^2x+\sin^2x=1 \] \[\cos^2x = 1-\sin^2x\] \[\frac{ 2\sin(\theta) }{ \sqrt{4(\cos^2(\theta))} }\]
UsukiDoll
  • UsukiDoll
\[\frac{2\sin(\theta)}{2\cos(\theta)}\]
zepdrix
  • zepdrix
\[\Large\rm \sqrt{4-4\sin^2x}\ne 2-2\sin x\]You silly billy Miriam -_-
UsukiDoll
  • UsukiDoll
I got tangent theta in return?!
UsukiDoll
  • UsukiDoll
I saw something weird when I saw that I mean can't we yank the 4 out and use a trig identity
Babynini
  • Babynini
Woah how'd you get tangent out of there? because the sin and cos are the same here?
UsukiDoll
  • UsukiDoll
\[\sqrt{4-4\sin^2x} \rightarrow \sqrt{4(1-\sin^2x)}\]
UsukiDoll
  • UsukiDoll
\[\sqrt{4\cos^2x} \rightarrow 2cosx \]
UsukiDoll
  • UsukiDoll
\[\frac{2sinx}{2cosx} \rightarrow \frac{sinx}{cosx} \rightarrow tanx\]
Babynini
  • Babynini
oou..I see!
UsukiDoll
  • UsukiDoll
you've skipped a step and that trickled down later on
UsukiDoll
  • UsukiDoll
\[(2\sin(\theta))^2 \rightarrow (2\sin(\theta))(2\sin(\theta))\]
UsukiDoll
  • UsukiDoll
\[4\sin^2(\theta)\]
UsukiDoll
  • UsukiDoll
you've neglected to take the 2sin(theta) to the second power... that's why everything became nonsense
Babynini
  • Babynini
Sorry, my internets really bad. yeah I was jumping around too much without checking o.0
Babynini
  • Babynini
Sowriee

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