10.4B  Solve Trig Eq Using Desmos

Problem Example 1 

      1.  Determine the value of x.  (Paper and pencil work)

               2 cos x = 1   [0, 2π]

                cos x = ½

               arccos(½) = π/3  and   5π/3

     2.  Using Desmos

              Using the solved equation above (in this case... cos x and 1/2),

               type the two expressions as equations:

                    y = cos x   (Note: This is the left side of the solved equation)

                    y = ½         (Note:  This is the right side of the solved equation)

      3.   Identify and label the ordered pairs for each point of intersection (Desmos).

     4.   Take a screenshot of your graph.

     5.    Check to determine if your algebraic solution matches the graph points of intersection.

Example 2

 1.  Determine the value of x.  (Paper and pencil work)

              4 sin2 x = 2   [0, 2π]

                   sin  x = ± sqrt(2)/2

                  arcsin(sqrt(2)/2) = π/4  and   3π/4

                  arcsin(-sqrt(2)/2) = 5pi/4 and 7pi/4

    2.  Using Desmos

             Using the solved equation above (in this case... sin x, sqrt(2)/2, -sqrt(2)/2),

                 type the expressions as equations:

                   y = sin x                 (Note: This is the left side of the solved equation)

                   y = sqrt(2)/2         (Note:  This is the right side of the solved equation)

                   y = -sqrt(2)/2       (Note:  This is the other value of the solved equation)

   3.   Identify and label the ordered pairs for each point of intersection (Desmos).

   4.   Take a screenshot of your graph.

   5.   Check to determine if your algebraic solution matches the graph points of intersection. 

         The image below is what you should be showing after you solve each equation.