Chapter 10.7 - Trigonometric Equations and Inequalities
Trigonometric Equations, trigonometric identities
TMM 002 PRECALCULUS (Revised March 21, 2017)
4c. Become fluent with conversions using traditional equivalency families.*
(e.g., (sin(𝑡))2+(cos(𝑡))2=1; (tan(𝑡))2+1=(sec(𝑡))2; sums/differences; products; double angle; Euler’s Formula (𝑒𝑖𝜃=cos(𝜃)+𝑖sin(𝜃)); etc.)
- The student can prove trigonometric identities.
- The student solves trigonometric equations.
- To solve √cos(4𝑡) = √sin(4𝑡), the student solves cos(4𝑡) =sin(4𝑡) and knows this procedure may result in extraneous solutions.
- The student solves |cos (2𝜃−3)| + 32 = 2 by rewriting the left-hand side as a piecewise-defined function.
- The student can rewrite formulas involving multiple occurrences of the variable to formulas involving a single occurrence. Write 𝑎sin(𝑤 𝑡)+𝑏cos(𝑤 𝑡) as 𝐴 sin (𝑤 𝑡+𝐵) or 𝐵 cos (𝑤 𝑡+𝐵). The student can rewrite sums as products to reveal attributes such as zeros, envelopes, and phase interference.
- The student can solve 2 𝑠𝑖𝑛2(𝑡)+7sin(𝑡)−4=0 on a given interval.
- The student can solve 𝑙𝑜𝑔4(sin (𝑡))+𝑙𝑜𝑔4(2sin(𝑡)+7)=1 on a given interval.
Trigonometric Equations and Inequalities
Review the concepts presented in earlier modules on
- properties of the six trigonometric functions, including their domains, range, and graphs
- properties of the inverse trigonometric functions
Learning Objectives: In this module we will learn about solving trigonometric equations.