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Trigonometry math 30pure

  1. Apr 26, 2008 #1
    [SOLVED] trigonometry math 30pure

    1. The problem statement, all variables and given/known data
    a student is given the following sinusoidal

    2 sin^2 (x)-5sinx=3

    2. Relevant equations

    1) Determine the solution to the equation , defined on the domain using a graphical approach over the domain 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2 [tex]\pi[/tex]. Give solutions as exact values.
    2) Determine the solution to the equation , defined on the domain using a algebraic approach over the domain 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2 [tex]\pi[/tex]. Give solutions as exact values.


    3. The attempt at a solution

    1) using my grafic calculator TI-83 plus i find this answers

    • Equation: Y1= 2 sin^2 (x)-5sinx, Y2= 3
    • Window: zoom trig
    • I/Z= find intersection points.
    • Answer: x= (-5)([tex]\pi[/tex])/6, (-1)([tex]\pi[/tex])/6, (7)([tex]\pi[/tex])/6, (11)([tex]\pi[/tex])/6
    2) now in this point i need help to do it algrbraticaly, i cant figure out how to do it or find any other example in my notes...
    is it using the equation y= a Sin[b(x-c)]+d??
    thanks
     
  2. jcsd
  3. Apr 26, 2008 #2
    note: oh it looks like where there is a pi as if it was n^pi but is not ...is actually N x pie ..(the pie is timing the number infront of it.)
     
  4. Apr 26, 2008 #3
    note that x only exists in the sin function, so you may do an appropriate substitution do get a more comfortable equation.
     
  5. Apr 27, 2008 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi cathoderay! :smile:

    (copy ² and π and anything else you like, for future use! … or, if you have a Mac, type alt-p for π. :smile:)

    Forget your TI-83+, and go for the simple answer …

    Hint: what is 2sin²x - 5sinx - 3 as a product (A sinx + B)(Csinx + D)? :smile:
     
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