10.4A  Solving Trig Equations

Most trigonometric equations can be divided into one of three types

         Type 1:  Equations involving the same trigonometric function squared. (i.e.  factoring)

              Examples:     

                          2 sin2(t) + sin(t) = 0

                          3 tan2(x) - 9 = 0

      Type 2:  Equations involving Pythagorean Identities with two different trigonometric functions.

                Examples:

                        2 sin2(t) - cos(t) = 1

                        cos(2x) -2 sin2(x) = 0

        Type 3:  Equations involving double angle formulas and another trigonometric function.

               Examples:

                       2 sin2 (t) - cos(t) = 1

                       cos(2x) + 3 = 5 cos(t)

  Type 1 - Simplifying Equations

         ~  It is possible to factor out a common term, in this case, sin(t).

          ~ Once factored, set factors equal to zero.

          ~ After determining the zeros, use the properties of inverse trig to determine the value(s) of t.

          ~ Plugin to determine if they are solutions.

Type 2 - Equations with Pythagorean Identities

        Given:  Two different trig functions.

          ~   Look at each to determine if an identity can be applied.

          ~   In the problem below, sin2x can be changed to its equivalent Pythagorean Identity.

          ~   Once the replacement is made, simplify the equation and factor.

          ~   Set factors equal to zero.

          ~   After determining the zeros, use the properties of inverse trig to determine the value(s) of t.