Use a graphing utility to approximate the equation's solutions in the interval [0, 2pi). If possible, find the exact solutions algebraically: 8 sin x cos x= 1

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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.