Step By Step Calculus » 5.6 - Trigonometry In Equations

show_hiddenExpand All [+]
In this section, we see how we can apply trigonometric identities to reduce algebraic expressions and thereby solve algebraic equations.
We also see the reverse application, that is how to use algebra to solve trigonometric equations. For solving such problems, we use the following general procedure called MESS.
Step 1 (Manipulate) Express the trigonometric equation in terms of a single trigonometric function.
Step 2 (Eliminate) Eliminate the trigonometric function by replacing it with a variable, say xx.
Step 3 (Solve) Solve the algebraic equation for xx and check for extraneous roots (if any).
Step 4 (Substitute) Substitute the trigonometric function back and find the corresponding solutions.