Trigonometric Equations

                     Lesson 1

                                                                                                                                                                          

                                                            Problem:   Solve: 5 Sin x + 2 = 0; x [0,2π]                                                          

                                                           

Solution    First, solve for Cos x.          

                                                            Step 1:                      

                     

                                                            Solution    5Sin x + 2 = 0

Step 2: 5Sin x = -2

Sin x = -2/5                 

                                                                                         

                                                            Solution    Now, Sine is negative in Quadrant III and Quadrant IV.

Step 3: Also, a sine value of 2/5 is a reference angle of 23.6.So;

consider the reference angle of 23.6 in quadrants III and IV.

x = 118.4 and 165.8 or 5π/7.6 and 7π/7.6                       

 

                                                            Solution     Answer: x = 118.4 and 165.8

Step 4:                                                    

Complete                                                                   

                                                                                                                               

                                                             Try two practice problems:  

 

                                                                                 Solve the following:

 

A.

If 0 ≤ x ≤ 2π,Solve the equation

6(cosx+2) = 4

B.

If 0 ≤ θ ≤ 2π,Solve the equation

10 tanθ + √6 = 3 tan θ

 

                                                                                               

 

 

 

 

 

        

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