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GSE Pre-Calculus 20152016 Unit One Information Curriculum Map: Unit Circle – Trigonometric Functions (Adv.Alg– Unit 5) Content Descriptors: Concept 1: Right Triangle Trig Review Concept 2: Unit Circle – Radians/Arc Length/Trig Ratios Concept 3: Co-terminal and Reference Angles Content from Frameworks: Trigonometric Functions Unit Length: Approximately 10 days TCSS – GSE Pre-Calculus – Unit 1 Curriculum Map Big Idea / Unit Understand all aspects of the unit circle. Unit Essential Questions: How does the unit circle apply to trig functions? Prerequisites: As identified by the GSE Frameworks Length of Unit 10 Days Right Triangle Trig. Concept 1 Right Triangle Trig Review GSE Standards MGSE9‐12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. (Special right triangles are included here.) Concept 2 Concept 3 Unit Circle – Radians/Arc Length/Trig Ratios Co-terminal and Reference Angles GSE Standards GSE Standards MGSE9‐12.F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. MGSE9‐12.F.TF.2 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. MGSE9‐12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. MGSE9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Lesson Essential Question What is the Pythagorean Theorem, and when is this theorem used? How are the sides and angles of right triangles related to each other? How can right triangle relationships be used to solve practical problems? TCSS Lesson Essential Question How do you find arc length of a circle? How do you find radians? 9/11/2015 Lesson Essential Question What are co- terminal and reference angles? How do I find the co-terminal and reference angles? 2 TCSS – GSE Pre-Calculus – Unit 1 Vocabulary 30-60-90 Special Right Triangle 45-45-90 Special Right Triangle Adjacent Angle Cosecant Cosine Cotangent Hypotenuse Opposite Reciprocal Functions Secant Sine Tangent Vocabulary Arc Length Degrees Odd/Even functions Periodicity Pi Radians Symmetry Unit Circle Arccosine Arcsine Arctangent Decreasing Domain Increasing Invertible function Resources – Concept 1 Resources – Concept 2 Trigonometry for any angle (Power Intro to converting degrees to radians (Power Point) What is a Radian Discovery Task Angles and Radian Measure (guided notes and practice ) KEY Unit Circle Blank Complete Degrees & Radians Conversion Practice Intro to Trig Practice Intro to the Unit Circle (Power Point) Unit Circle Teacher Notes Practice (basics and the unit circle) Exact Trig Value Chart Unit Circle/Trig Practice KEY More Unit Circle Practice Point) Right Triangle Trig Review notes (guided notes and practice) Right Triangle Applications Review (guided notes and practice) Trig Review Practice Worksheet KEY Trig Cut Up Puzzle Differentiated Activities Concept 1 Unit Guided Notes/ Vocabulary Differentiated Activities Concept 2 Resources – Concept 3 Point on a Terminal Side Notes Graphic Organizer (culminating) Differentiated Activities Concept 3 Differentiated Unit Circle Activity Activities/Practice (highly recommended) TCSS 9/11/2015 3 TCSS – GSE Pre-Calculus – Unit 1 Unit 1 Checklist – Unit Circle-Trig Functions Good luck to ________________________Date_______ Period___ Keep this list handy and refer to it periodically to see how you are doing. If you know how to each of these you should do well on an exam. Unit 1 – Unit Circle - Trig Functions self-assessment and tracker In this unit I : sort of really • can accurately complete the unit circle. • can use the unit circle to find trig ratios for any degree or radian measure. • can convert from degree to radian measure. • can find arc length. • can compute reference and co-terminal angles. TCSS 9/11/2015 4