TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Periodic Functions and Trigonometry (Allow approximately 4-5 weeks for instruction, review, and assessment) Domain: Number and Quantity Cluster: Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling. Domain: Trigonometric Functions Cluster: Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Enduring Understanding(s): Periodic behavior repeats over intervals of constant length. The amplitude of a periodic function is half the difference of the maximum and minimum values of the function. Essential Question(s): Why would a heart rate monitor be an example of a periodic function? Objective(s): Students will identify cycles and periods of a periodic function. Students will find the amplitude of periodic functions. Students apply geometric concepts in modeling situations. Use the following Lesson(s) and task(s) to introduce concepts/build conceptual understanding. , Use the textbook resources to address procedural and fluency. Pearson 13-1 Exploring Periodic Data Vocabulary Periodic function, cycle, period, amplitude Writing in Math/Discussion Functions that repeat over time are common in everyday life. The English language has many words that stand for periods of time. Name a few terms and state the period of time from which the term is derived.
Students understand that some periodic behavior is too complicated to be modeled by simple trigonometric functions. Students will graph and write equations of translations of trigonometric functions Domain : Building Functions Cluster: Build new functions from existing functions F-BF.B.3 Domain: Interpreting Functions Cluster: Interpret functions that arise in applications in terms of the context Domain: Interpreting Functions Cluster: Analyze functions using different representations F-IF.C.7e F-IF.C.9 Enduring Understanding(s): Cosine, sine, and tangent have reciprocals named secant, cosecant, and cotangent. Reciprocal can be evaluated on what has been previously learned about sine, cosine, and tangent. The graphs of reciprocal trigonometric functions have asymptotes when their denominators are equal to zero. Essential Question(s): What error regarding secant and cosecant is easy to make? Objective(s): Students will evaluate reciprocal trigonometric functions. Students will graph reciprocal trigonometric functions. Use the textbook resources to address procedural skill and fluency. Pearson 13-8 Reciprocal Trigonometric Functions Glencoe 13.9 Inverse Trigonometric Functions Additional Resources Lesson Videos: Vocabulary Cosecant, secant, cotangent Journaling/Prompt Compare and contrast the graphs y = sec x and y = csc x. Trigonometric Identities (Allow approximately 1-2 weeks for instruction, review, and assessment) Domain: Trigonometric Functions Cluster: and apply trigonometric identities. Prove the Pythagorean identity sin2 (θ) + cos 2 (θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) Enduring Understanding(s): trigonometric identities can be used to verify other identities. Trigonometric identities can be used to simplify trigonometric Use the following Lesson(s) and task(s) to introduce concepts/build conceptual understanding. engageny Algebra II Module 2, Topic B Lesson 15 Vocabulary Trigonometric Identity Journaling/Prompt Develop your own trigonometric identity.