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Trigonometry math 30pure

  • Thread starter cathoderay
  • Start date
16
0
[SOLVED] trigonometry math 30pure

1. Homework Statement
a student is given the following sinusoidal

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

2. Homework 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
 

Answers and Replies

16
0
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.)
 
144
0
note that x only exists in the sin function, so you may do an appropriate substitution do get a more comfortable equation.
 
tiny-tim
Science Advisor
Homework Helper
25,789
249
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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