Lesson 5: 5.5 Multiple-Angle and Product-to-Sum Formulas

How do you rewrite trigonometric expressions that contain functions of multiple or half-angles, or functions that involve squares or products of trigonometric expressions?

double-angle formula
power-reducing formula
half-angle formula
product-to-sum formula
sum-to-product formula

HSF-TF.C.10 - Prove the half angle and double angle identities for sine and cosine and use them to solve problems

Use Khan Academy resources.

Students will combine all of their prior knowledge of trigonometric functions and identities with the new formulas in this section to solve more trigonometric equations.

You can use a variety of trigonometric formulas to rewrite trigonometric functions in more convenient forms. For instance, a half-angle formula can be used to determine the apex angle of a sound wave cone caused by the speed of an airplane.

Some students may incorrectly rewrite power-reducing formulas.

Be sure that your students are able to recognize all three forms of the double-angle formula for cos2u. Consider asking your students to show the equivalence of all three forms as an activity during class.
Students have learned so many trigonometric identities up to this point that they may e able to solve the problems in this section using different methods. Have students solve problems multiple ways and compare methods.
Remind students to always write the formula used and to show each step of their work to help eliminate errors.

Use common assessments.

Pre-Calculus with Limits resources.