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:    



Example 2:    



                    At this point we know that :


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.




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.




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.


             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.