half-angle identities GSE Pre-Calculus: Unit 4 Trigonometric The power-reducing formula for Identities the sine squared of an angle Derive and use the product-to-sum and The power-reducing formula for Double-Angle Identities for Sine, Cosine, and sum-to-product identities Tangent p. 38 the cosine squared of an angle Solve applications using these identities The Cosine Double-Angle: A Man with Many Identities p. 43 Domain: Building Functions Enduring Understanding(s); 6.5 Inverse Trigonometric Functions and their Vocabulary Applications (Coburn) Cluster: Build new functions from existing Inverse functions Exponential and logarithmic functions are functions. 5.7 Inverse Trigonometric Functions (Blitzer) inverse functions. Find inverse functions (including exponential Mathematical functions can be used to Writing in Math and logarithmic) solve real world applications. Additional Resource(s) Explain why, without restrictions, no Algebra & Trigonometry (Coburn), 2nd Edition trigonometric function has an inverse. (Exercise Videos, Lecture Videos, Essential Question(s) Graphing Calculator Videos, How can the graph od y = sin-1x be obtained How can graphs and equations of PowerPoint Presentations) from the graph of the restricted sine function? functions and their inverses help us to interpret real world problems? How can analytic and graphical methods Describe the restriction on the sine function be used to support each other in the so that it has an inverse function. solution of a problem? Task(s) Describe the restriction on the cosine function Objective(s): so that it has an inverse function. Inverse Trigonometric Functions (p.31) Students will: Find and graph the inverse sine function and evaluate related expressions Find and graph the inverse cosine and tangent functions and evaluate related expressions Apply the definition and notation of inverse trig functions to simplify compositions
half-angle identities Derive and use the product-to-sum and sum-to-product identities Solve applications using these identities GSE Pre-Calculus: Unit 4 Trigonometric Identities Double-Angle Identities for Sine, Cosine, and Tangent p. 38 The Cosine Double-Angle: A Man with Many Identities p. 43 The power-reducing formula for the sine squared of an angle The power-reducing formula for the cosine squared of an angle Domain: Building Functions Cluster: Build new functions from existing functions. Find inverse functions (including exponential and logarithmic) Enduring Understanding(s); Exponential and logarithmic functions are inverse functions. Mathematical functions can be used to solve real world applications. Essential Question(s) How can graphs and equations of functions and their inverses help us to interpret real world problems? How can analytic and graphical methods be used to support each other in the solution of a problem? Objective(s): Students will: Find and graph the inverse sine function and evaluate related expressions Find and graph the inverse cosine and tangent functions and evaluate related expressions Apply the definition and notation of inverse trig functions to simplify compositions 6.5 Inverse Trigonometric Functions and their Applications (Coburn) 5.7 Inverse Trigonometric Functions (Blitzer) Additional Resource(s) Algebra & Trigonometry (Coburn), 2nd Edition (Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Task(s) Inverse Trigonometric Functions (p.31) Vocabulary Inverse functions Writing in Math Explain why, without restrictions, no trigonometric function has an inverse. How can the graph od y = sin-1x be obtained from the graph of the restricted sine function? Describe the restriction on the sine function so that it has an inverse function. Describe the restriction on the cosine function so that it has an inverse function.
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