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Department: Mathematics Course: AAT-H Standards: Common Core State Standards Unit 13: Chapter 7 Extend the domain of trigonometric functions using the unit circle Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle Model periodic phenomena with trigonometric functions Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline Prove and apply trigonometric identities Prove the Pythagorean identity and use it to calculate trigonometric ratios Stage 1: Desired Results Understandings We commonly think of Trigonometry as the study of measurements in a triangle, but it's use extends to the applications of trigonometric relationships as functions of real numbers which can be applied to a vast number of physical phenomena involving rotations and vibrations. The trigonometric functions can be used to solve for lengths and angle measures in triangles, even in real-life situations. Essential Questions How can you convert between radians and degrees? Knowledge & Skill See handout attached How can we use the trigonometry identities to solve for missing information? Where might you use trigonometry in reallife settings? Stage 2: Assessment Evidence In-class problems, verbal response, homework assignments, Problems of the Week, clean-up days for selfassessment, observation, quizzes, test Performance Task Summary Homework assignments Problems of the Week Quizzes Test Rubric Titles Problems of the Week Wrapping Function Values Quiz Trigonometric Values Quiz Trigonometry Unit A Exam Self-assessment of objectives Review of lessons Homework corrections Problem of the Week corrections Partner/Group checks Quiz corrections Other Evidence, Summarized Other assessment information will be obtained through observations, classroom participation, class discussions, and partner/group interactions. The unit assessment will be graded, gathered, and analyzed district wide. Stage 3: Learning Activities In-class problems Group activities Board work Class discussion Using the graphing calculator Unit 13: Chapter 7 Knowledge and Skills Objectives I can… Describe an angle and convert between radian and degree measures Evaluate trigonometric functions of any angle Use the fundamental trigonometric identities Sketch the graphs of trigonometric functions Sketch translations of sine and cosine function graphs Evaluate the inverse trigonometric functions Evaluate compositions of trigonometric functions Use fundamental trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions Verify trigonometric identities Use standard algebraic techniques and inverse trigonometric functions to solve trigonometric equations Use sum and difference formulas, multiple-angle formulas, power-reducing formulas, half angle formulas, and product-to-sum formulas to rewrite and evaluate trigonometric functions Vocabulary Trigonometry Initial side Terminal side Standard position Positive angles Negative angles Coterminal angles Degree Radian Linear speed Angular speed Sine Cosine Tangent Cosecant Secant Cotangent Reference angle Period Amplitude Phase shift Damping factor Inverse sine Inverse cosine Inverse tangent Angle of elevation Angle of depression Bearings Simple harmonic motion Sum and difference formulas Reduction formulas Power-reducing formulas Half-angle formulas Sum-to-product formulas