Trigonometric Equations

In earlier sections we examined trigonometric identities, which are equations involving trigonometric functions that are satisfied by all values of the variable for which both sides of the equality are defined. In this section we examine conditional trigonometric equations, that is, equations that are true for only certain values of the variable. When solving for the solutions for these equations there might be an infinite amount of answers because of the periodicity of the trigonometric functions. In general, to obtain solutions of an equation such as sin x=radical 2/2, it is more convenient to use a unit circle and reference angles rather than a graph of the trigonometric function. When solving an equation, if you divide by an expression containing a variable, you may lose some solutions of the original equation. To prevent the loss of a solution you must determine the values that make the expression zero and check to see whether they are solutions of the original equation.