csc x from the graph. What is the range? Identify and discuss important characteristics of y = tan t and y = cot t Graph y = A tan(Bt) and y = A cot(Bt) with What does it mean to solve a right triangle? various values of A and B Solve applications of y = tan t and y = cot t Explain how to find one of the acute angles of Apply vertical translations in context a right triangle if two sides are known? Apply horizontal translations in context Solve applications involving harmonic motion Trigonometric Identities, Inverses, and Equations (Allow approximately 3 weeks for instruction, assessment, and review) Domain: Trigonometric Identities Enduring Understanding(s) 6.1 Fundamental Identities and Families of Vocabulary Identities (Coburn) Cluster: Apply trigonometric identities to Identity Understand the relationship between right rewrite expressions and solve equations. 6.2 Constructing and Verifying Identities triangle trigonometry and unit circle (Coburn) trigonometry G-TI.1 Apply trigonometric identities to verify Writing in Math identities and solve equations. Identities 6.1 Verifying Trigonometric Identities (Blitzer) Use the unit circle to define trigonometric Create a toolbox for all of the different include: Pythagorean, quotient, functions. trigonometric identities. sum/difference, double-angle, and half-angle. There are many instances of periodic Additional Resource(s) data in the world around us and Algebra & Trigonometry (Coburn), 2nd Edition Explain how to verify an identity. trigonometric functions can be used to (Exercise Videos, Lecture Videos, model real world data that is periodic in Graphing Calculator Videos, nature. Describe two strategies that can be used to PowerPoint Presentations) The inverses of sine, cosine and tangent verify identities. functions are not functions unless the domains are limited. Task(s) Essential Question(s) How do you evaluate trigonometric Hopewell Geometry functions for given values, periods, and intervals? How trigonometric functions relate to the Accelerated Math III: Unit 6 Trigonometric unit circle? Identities, Equations, and Applications How do we model real-world scenarios to
Identify and discuss important characteristics of y = tan t and y = cot t Graph y = A tan(Bt) and y = A cot(Bt) with various values of A and B Solve applications of y = tan t and y = cot t Apply vertical translations in context Apply horizontal translations in context Solve applications involving harmonic motion csc x from the graph. What is the range? What does it mean to solve a right triangle? Explain how to find one of the acute angles of a right triangle if two sides are known? Trigonometric Identities, Inverses, and Equations (Allow approximately 3 weeks for instruction, assessment, and review) Domain: Trigonometric Identities Cluster: Apply trigonometric identities to rewrite expressions and solve equations. G-TI.1 Apply trigonometric identities to verify identities and solve equations. Identities include: Pythagorean, quotient, sum/difference, double-angle, and half-angle. Enduring Understanding(s) Understand the relationship between right triangle trigonometry and unit circle trigonometry Use the unit circle to define trigonometric functions. There are many instances of periodic data in the world around us and trigonometric functions can be used to model real world data that is periodic in nature. The inverses of sine, cosine and tangent functions are not functions unless the domains are limited. Essential Question(s) How do you evaluate trigonometric functions for given values, periods, and intervals? How trigonometric functions relate to the unit circle? How do we model real-world scenarios to 6.1 Fundamental Identities and Families of Identities (Coburn) 6.2 Constructing and Verifying Identities (Coburn) 6.1 Verifying Trigonometric Identities (Blitzer) Additional Resource(s) Algebra & Trigonometry (Coburn), 2nd Edition (Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Task(s) Hopewell Geometry Accelerated Math III: Unit 6 Trigonometric Identities, Equations, and Applications Vocabulary Identity Writing in Math Create a toolbox for all of the different trigonometric identities. Explain how to verify an identity. Describe two strategies that can be used to verify identities.