
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.
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!!! 

Solving Quadratic Equations: 
Remember to first solve for the trig function and then solve for the angle value.
Solution:
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.
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.
.
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. 

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