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Solving Trigonometric Equations with multiple solutions

  • Thread starter Sadriam
  • Start date
8
0
1. Homework Statement
Solve each equation for solutions on the interval 0 ≤ x ≤ 2∏.
Code:
2 sin x = √3
3. The Attempt at a Solution
Okay so I was able to solve this one:

  • 2 sin x = √3
  • sin x = (√3) / 2

So i got x = ∏/3 ; 2∏/3 ; 4∏/3 ; 5∏/3

I substituted the x's into the original problem, and ∏/3 and 2∏/3 give +(√3). The other two give -(√3). Are the one's that give negative results also solutions? If so, is this only true for (±√x), or is the sign always a significant factor?
 

HallsofIvy

Science Advisor
Homework Helper
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No, if [itex]sin(x)= -\sqrt{3}/2[/itex] then [itex]2sin(x)= -\sqrt{3}[/itex] which is NOT the original equation. Those values of x do NOT satisfy the equation and are NOT solutions. In particular, [itex]\sqrt{a}[/itex] is NOT the same as either [itex]-\sqrt{a}[/itex] or [itex]\pm\sqrt{a}[/itex].
 
8
0
Thank you for clarifying (:
 

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