Methods for Solving Trigonometric Equations MathBitsNotebook.com Topical Outline | Algebra 2 Outline | MathBits' Teacher Resources Terms of Use   Contact Person: Donna Roberts

When the trig functions has a power (a numerical exponent), it will have to be solved by extracting square roots (cube roots, etc) or by factoring.

Solution:    

Solution:                 Now,

Now, tan x = 0 implies that x = 0, π, 2π . (See graph at the right.) Since the sine function has maximum and minimum values of +1 and -1, has no solutions. Thus the answer x = 0, π, 2π the only solution.
In this 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 at the right would result. 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.

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

Solution:    

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

 
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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:

For help with trigonometric equations on your calculator, click here.