Solving Trigonometry Equation Algebraically

In summary, a student was given a sinusoidal equation and was asked to find the solutions on the given domain using both a graphical and algebraic approach. Using a TI-83 Plus calculator, they found the intersection points to be x= (-5)(π)/6, (-1)(π)/6, (7)(π)/6, (11)(π)/6. However, they needed help with the algebraic approach and were advised to find a simpler solution by factoring the equation into a product.
  • #1
cathoderay
16
0
[SOLVED] trigonometry math 30pure

Homework Statement


a student is given the following sinusoidal

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

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.


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 can't 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
 
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  • #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.)
 
  • #3
note that x only exists in the sin function, so you may do an appropriate substitution do get a more comfortable equation.
 
  • #4
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:
 

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles.

What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. They are commonly abbreviated as sin, cos, and tan respectively.

How is Trigonometry used in real life?

Trigonometry has many real-life applications, such as in architecture, navigation, engineering, and physics. It is used to calculate distances, heights, angles, and other measurements in various fields.

What are the identities in Trigonometry?

The most commonly used identities in Trigonometry are Pythagorean identities, reciprocal identities, quotient identities, and double-angle identities. These identities help simplify and solve trigonometric equations.

What is the difference between Trigonometry and Geometry?

Trigonometry deals specifically with the study of triangles and their relationships, while Geometry is a broader branch of mathematics that deals with the study of shapes, sizes, and positions of objects in space.

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