minatsukisaya95
  • minatsukisaya95
how to find the solution in the interval of 0 to 360 deg for 2cos u+cos 2u=0
Trigonometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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lncognlto
  • lncognlto
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DebbieG
  • DebbieG
I think if you make a substitution using the identity: \(\Large \cos2u=2\cos^2u-1\) Then you will have an equation of quadratic type and can solve with quadratic equation methods.
minatsukisaya95
  • minatsukisaya95
i have done that but it is not real number

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DebbieG
  • DebbieG
You should get 2 solutions for cos(u).... then use the inverse function to find u. Can you show your work to solve the quadratic? You should get 2 irrational solutions.
minatsukisaya95
  • minatsukisaya95
yep i get two irrational solution from that how do i do next
DebbieG
  • DebbieG
\[\Large 2\cos u+\cos 2u=0\]\[\Large 2\cos u+2\cos^2u-1=0\] disriminant =\(\large b^2-4ac=4-4(2)(-1)=4+8=12\) so should have 2 irrational solutions.
DebbieG
  • DebbieG
OK, remember that those are solutions for cosu. So you have cos(u)=a You want u. and you know the cosine of u. What "tool" (think of a function that you can use) takes the COSINE VALUE of an angle as the input, and gives you the ANGLE MEASURE as the output?
DebbieG
  • DebbieG
These are your solutions for the quadratic? \[\Large \cos u=\frac{ -1\pm \sqrt{3} }{ 2}\]
minatsukisaya95
  • minatsukisaya95
oh ok so the two solution is the exact value of cos u ok ok i got it thank u
DebbieG
  • DebbieG
you're welcome. :)
goformit100
  • goformit100
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