Solving Trigonometry Equation Algebraically

[cathoderay]

[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 $$\leq$$ x $$\leq$$ 2 $$\pi$$. Give solutions as exact values.
2) Determine the solution to the equation , defined on the domain using a algebraic approach over the domain 0 $$\leq$$ x $$\leq$$ 2 $$\pi$$. 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)($$\pi$$)/6, (-1)($$\pi$$)/6, (7)($$\pi$$)/6, (11)($$\pi$$)/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

 

[cathoderay]

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.)

 

[Kurret]

note that x only exists in the sin function, so you may do an appropriate substitution do get a more comfortable equation.

 

[tiny-tim]

Hi cathoderay!

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

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

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