Lesson 3: 5.3 Solving Trigonometric Equations

How do you solve trigonometric equations written in quadratic form or containing more than one angle?

square root
factoring
quadratic
inverse

HSF-TF. B. 7 - Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

Use Khan Academy resources.

Students will combine algebraic techniques for solving equations with the fundamental trigonometric identities to solve trigonometric equations. They will find both specific solutions and general solutions of trigonometric equations.

You can use trigonometric equations to solve a variety of real-life problems. For instance, you can solve a trigonometric equation to help answer questions about monthly sales of snowboards.

Some students may not include all possible solutions from each quadrant. Remind students that the solutions must be checked against the range of the function and the specified interval. If no interval is specified, solutions must include multiples beyond the first period.
When solving a multiple-angle equation, some students may incorrectly multiply or divide each side of the equation by the coefficient of the angle and ignore the trigonometric function. Remind students that they must first solve for the angle.

Encourage students to list out a few multiples of the solution so they can see the pattern of solutions in order to write the general solution.
Your students may find working with trigonometric equations difficult at first. Suggest that they write or visualize an algebraic model initially, translate the model into trigonometric terms, and then solve for x.
Remind students to use their prior knowledge of the fundamental identities to rewrite the equation before solving.
Consider having your students check their solutions with a graphing utility. This will help reinforce the fact that there are many solutions, and will demonstrate why.

Use common assessments.

Pre-Calculus with Limits resources.