Methods for Solving Trigonometric Equations

Topical Outline | Algebra 2 Outline | MathBits' Teacher Resources

Terms of Use   Contact Person: Donna Roberts
Trigonometric Equations with Powers:

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.

ex1     trigeq44

Solution:     trigeq45


ex2     ;

Solution:     trigeq45            Now, trigeq45

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, d 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!!!




Solving Quadratic Equations:

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

ex3   d

Solution:    s


Using Identities in Equations 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.

ex4    a

Solution:    d



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.

ex5   a

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.
MathBits Calculator Pages


NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
and is not considered "fair use" for educators. Please read the "Terms of Use".