anonymous
  • anonymous
Solve for x: sin2x=sin x, 0≤x≤2π
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Psymon
  • Psymon
Youd have to use an identity on the sin2x. Because you cant have different angles when youre solving these. SO you usr a double angle formul on sin2x to get everything int erms of just a single x angle. Do you know the double angle identity for sin2x?
anonymous
  • anonymous
No sorry
Psymon
  • Psymon
Well, a lot of these you may be forced to remember unfortunately, so might as well write them down when they come up. So, sin2x = 2sinxcosx. Meaning youre actually trying to solve 2sinxcosx = sinx

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anonymous
  • anonymous
So using that formula the equation will become 2sinxcosx=sinx then divide both sides by sinx which will leave you with sinxcosx as your answer
Psymon
  • Psymon
Well first off if you divide both sides by sinx you have 2cosx = 1. But even then you still have more work to do. You cant just solve for cosx or sinx, you have to solve for the actual x.
Psymon
  • Psymon
So what we need to do is get the cosx by itself, just as if we were solving for x. So that means I also want to divide both sides by 2 to give us cosx = 1/2 Now, do you have a unit circle chart handy?
anonymous
  • anonymous
Yes
Psymon
  • Psymon
Alright, cool. So there are two angles on the unit circle where cosx = 1/2. Just gotta find them.
anonymous
  • anonymous
Okay is it (cos, sin) on the unit circle
Psymon
  • Psymon
Yes, cos is x, sin is y
anonymous
  • anonymous
Okay so the angle would be 60
Psymon
  • Psymon
thats one of the 2.
anonymous
  • anonymous
Okay and the other is 300
Psymon
  • Psymon
Yep, those are your two answers then :3
anonymous
  • anonymous
So do you just write is as x=300 and 60 degrees
Psymon
  • Psymon
Pretty much.
anonymous
  • anonymous
Thank you so much!
Psymon
  • Psymon
Yeah. np ^_^

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