anonymous
  • anonymous
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Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I think you can use calculator for solving this problem
Callisto
  • Callisto
2sin(2θ)=0.92, sin(2θ)=0.92/2 2θ = 27.387 θ = 13.6935 180°≤θ≤360° θ in quad. III = 180° +θ = 193.6935 θ in quad IV = 360 -θ = 346.3065 Do the checking, 2sin(2θ) = 2sin 2(193.6935) = 0.92 2sin(2θ) = 2sin2(346.3065) = -0.92 (rejected) So θ = 193.6935 Not sure if it works, i just guess..
anonymous
  • anonymous
I'm with Callisto :)

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Callisto
  • Callisto
sin(2θ)=0.92/2 sin(2θ)= 0.46 (2θ) = sin^-1 (0.46) (2θ) = 27.387
Callisto
  • Callisto
you should also note that i miss out 'sin' to get 27.387 just now
anonymous
  • anonymous
I got exact the result!
anonymous
  • anonymous
2sin(2θ)=0.92 :. sin(2θ)=0.46 :.2θ=0.477995 rad :.θ=0.238997599 rad
anonymous
  • anonymous
:θ=0.238997599 rad is also 13.69355375 degree
Callisto
  • Callisto
@duy11nv But 180°≤θ≤360°
anonymous
  • anonymous
I get it now, thank you :D
anonymous
  • anonymous
@callisto you right
Callisto
  • Callisto
Nah.. convert the answer in degree into rad if you need
anonymous
  • anonymous
But how do you get the second answer now?
anonymous
  • anonymous
\[\pi\] radian ~ \[180^{0}\] so x radian ~ \[(x: \pi)*180\]
anonymous
  • anonymous
I know that the second answer is 4.4705716...rad, and 256.1448889753...°
anonymous
  • anonymous
But how?
anonymous
  • anonymous
Using properties of sine fuction, that sin(Pi-x)=sin(x) or sin(180-x)=sin(x)
EarthCitizen
  • EarthCitizen
you're to have two anwsers for theta
Callisto
  • Callisto
270 - θ ?!
anonymous
  • anonymous
But how do I write that down like you did before " θ in quad. III = 180° +θ = 193.6935"
EarthCitizen
  • EarthCitizen
@ricnus, don't you have the answer so you can know which solutions are correct ?
anonymous
  • anonymous
I know what the solutions are only because of a calculator, but I need to know how to do this
EarthCitizen
  • EarthCitizen
you need to expand the equation to give a quadratic expression \[2\sin(2\theta) = 4\sin \theta \cos \theta\]
EarthCitizen
  • EarthCitizen
i suggest you use tan theta
EarthCitizen
  • EarthCitizen
\[4\sin \theta \cos \theta = (4\tan \theta)/(1+\tan ^{2}\theta)\] @ ricnus
campbell_st
  • campbell_st
the values for theta are pi + 0.2389... and 2pi - 0.2389..... this will give 2theta = 2(pi + 0.2389...) and 2(2pi - 0.2389...) which woll put the angles in the 1st and 2nd quadrants sin is positive in those quadrants and will result in the fact that \[2\sin(2\theta) =0.92\] the domain restriction is on theta and not 2 theta...
EarthCitizen
  • EarthCitizen
\[\therefore Tan(\theta) =y\]
anonymous
  • anonymous
@EarthCitizen and how does (4tanθ)/(1+tan^2(θ)) help, I am so confused by this
EarthCitizen
  • EarthCitizen
@ricnus it's an identity, didn't you do that in class before doing this question ?
kropot72
  • kropot72
The answer by campbell_st is correct. I suggest you focus on his explanation.
EarthCitizen
  • EarthCitizen
you should have\[0.92y ^{2}-4y+0.92=0\]
anonymous
  • anonymous
Yes I know that, that is an identity, but how does it help it?
Callisto
  • Callisto
@campbell_st But for this: 2(2pi - 0.2389...), i got a -ve result, ...
anonymous
  • anonymous
Oh, making it into a quadratic :D
EarthCitizen
  • EarthCitizen
solve for y, by using quadratic formula
EarthCitizen
  • EarthCitizen
@ricnus yep
anonymous
  • anonymous
Sorry, I understood how you got the identity, but I only just realised what it could be used for :D
EarthCitizen
  • EarthCitizen
yh, no p! the equation should give you y = 4.10417 or 0.243655
EarthCitizen
  • EarthCitizen
recall, \[y = ta n \theta\]
EarthCitizen
  • EarthCitizen
you use that to find theta by taking the inverse of tan
EarthCitizen
  • EarthCitizen
Hence, \[ta n \theta = 4.10417, ta n \theta=0.243655\]
EarthCitizen
  • EarthCitizen
solve for theta
EarthCitizen
  • EarthCitizen
\[\theta = 76.31^{o}, 14^{o}\]
EarthCitizen
  • EarthCitizen
no, it has to be within the range of 180 and 360
EarthCitizen
  • EarthCitizen
what are the answers in your text book ?

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