More Methods for Solving Trigonometric Equations
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

 

Trigonometric Equations involving Powers:

When the trig function has a power, it will have to be solved by extracting square roots or  factoring.

Example 1:    

                     Solution: 
                                        

 

Example 2:    

                     Solution:

                                                                         

                    At this point we know that :

                                                  



Now, implies that (see graph).  Since the sine function has maximum and minimum values of +1 and -1, has no solutions.
Thus the answer is the only solution.

  

 

In this last example, you may have been tempted to divide all the terms by tan x to simplify the equation.  If this had been done, the equation would have been:

We lost the tan x term and its solution by dividing by tan x.
Not a good move!!!

 

Solving Quadratic Equations:

Remember to first solve for the trig function and then solve for the angle value.

Example:  

                     Solution:
                                               


 

Using Identities in Equation Solving:

If there is more than one trig function in the equation,
identities are needed to reduce the equation to a single function for solving.

Example:   

         Solution:
                          

 

Using Quadratic Formula with Trig Equations:

There are trig equations, just like there are normal equations, where factoring does not work!!   In these cases, the quadratic formula comes in handy.

Example: 
                                       

             Solution:  Since there are two trig functions in this problem, we need to use an identity
                             to eliminate one of them.                       
                            

Using the quadratic formula, we get:

                                   


                                                 

How to use your
TI-83+/84+ graphing calculator  to solve trigonometric equations.
Click calculator.