Use the identity 2sinxcosx = sin2x. The equation becomes: 4(2sinxcosx) = 1
4sin2x = 1
sin2x = .25 (divide both sides by 4
2x = inverse sin .25
x = (inverse sin .25)/2 = .13
Since sine is periodic there will be another answer related to this first one.
2x = (inverse sin .25) + 2π
x = (inverse sin .25)/2 + π = 3.27
Two more solutions are possible because sine is also positive in quad 2.
x = (π - (inverse sin .25))/2 = 1.44
add π to this answer to get your final answer 4.57
So there are 4 solutions: .13, 1.44, 3.27 and 4.59
On a graphing calculator make sure you are in radian mode. Set the x axis to (0, 6.28) and the y axis to (-10, 10) (y doesn't really matter)
Graph y = 8sinxcosx - 1
Use 2nd calc and choose zero to find the four x intercepts. (one at a time)They are the same as the algebraic solution.