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!!!

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.

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Frederick Roberts
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