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!!!

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.

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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: