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Mr. Wolf Pre-Calculus Monday 12/22/08 Grades 11-12 Unit 5: Graphs & Inverses of Trigonometric Functions Review Unit 5 Materials and Resources: Warm-up (1 per student) Unit 5 Study Guide (1 per student) Exit ticket (1 per student) PA Standards Addressed: Instructional Objectives: Students will be able to solve real world applications of trigonometric functions. Students will be able to review for the Unit 5 Test. Time 10 min 1 min 45 min Activity Warm-up Agenda Real World Applications 35 min Unit 5 Review 1 min 5 min Agenda Conclusion Homework: Study for Unit 5 Test Lesson Reflection: Description Pass out the warm-up and review solutions. Review the goals for the day. Modeling: Guiding: Independent Practice: Assessment: Modifications: Students with special needs… Advanced students… Modeling: Guiding: Independent Practice: Assessment: Modifications: Students with special needs… Advanced students… Revisit goals and identify whether they were met. Pass out the Exit Ticket and collect at the bell. Pre-Calculus Fall 2008 Name: ________________________ Warm-up A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool. Pre-Calculus Fall 2008 Name: ________________________ Warm-up A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool. Pre-Calculus Fall 2008 Name: ________________________ Unit 5 Study Guide Section 4.5 Graphs of Sine and Cosine Functions Sketch graphs of y sin x and y cos x Describe the effects of a, b, c, and d values on the shifts and transformations of y d a sin( bx c) and y d a cos(bx c) Identify domain, range, amplitude, period, maximum, minimum, x-intercepts, yintercepts of sine and cosine curves Sketch graphs of sine and cosine curves Write the equations of sine and cosine graphs Section 4.6 Graphs of Other Trigonometric Functions Sketch graphs of y sec x , y csc x , y tan x , and y cot x Describe the effects of a, b, c, and d values on the shifts and transformations of y d a sec(bx c) , y d a csc(bx c) , y tan( bx c) , and y cot( bx c) Identify domain, range, amplitude, period, asymptotes, maximum, minimum, xintercepts, y-intercepts of secant, cosecant, tangent, and cotangent curves Sketch graphs of secant, cosecant, tangent, and cotangent curves Write the equations of secant, cosecant, tangent, and cotangent graphs Section 4.7 Inverse Trigonometric Functions Define the domain and range of the inverse trigonometric functions Evaluate arcsin, arcos, and arctan functions Evaluate compositions of inverse trigonometric functions with basic trigonometric functions at standard angles (0, 30º, 60º, 90º, etc.) Evaluate compositions of inverse trigonometric functions with basic trigonometric functions at non-standard angles by sketching a right triangle Section 4.8 Applications and Models Solve a right triangle by applying SOHCAHTOA ratios and the Pythagorean Theorem to find all side lengths and angle measurements Apply solving a right triangle in real world situations Apply solving a right triangle to determine directional bearings Identify amplitude, frequency, and period in order to write the equations of simple harmonic motion Solve simple harmonic motion problems Pre-Calculus Fall 2008 Name: ________________________ Exit Ticket Identify the topics you will focus your studying on tonight: Sketching graphs of trigonometric functions Describing the effects of a, b, c, and d values on the shifts and transformations Identifying domain, range, amplitude, period, maximum, minimum, x-intercepts, y-intercepts of trigonometric function graphs Writing the equations of trigonometric function graphs Defining the domain and range of the inverse trigonometric functions Evaluating arcsin, arcos, and arctan functions Evaluating compositions of inverse trigonometric functions with basic trigonometric functions at standard angles (0, 30º, 60º, 90º, etc.) Evaluate compositions of inverse trigonometric functions with basic trigonometric functions at non-standard angles by sketching a right triangle Apply solving a right triangle in real world situations Identify amplitude, frequency, and period in order to write the equations of simple harmonic motion Solve simple harmonic motion problems Pre-Calculus Fall 2008 Name: ________________________ Exit Ticket Identify the topics you will focus your studying on tonight: Sketching graphs of trigonometric functions Describing the effects of a, b, c, and d values on the shifts and transformations Identifying domain, range, amplitude, period, maximum, minimum, x-intercepts, y-intercepts of trigonometric function graphs Writing the equations of trigonometric function graphs Defining the domain and range of the inverse trigonometric functions Evaluating arcsin, arcos, and arctan functions Evaluating compositions of inverse trigonometric functions with basic trigonometric functions at standard angles (0, 30º, 60º, 90º, etc.) Evaluate compositions of inverse trigonometric functions with basic trigonometric functions at non-standard angles by sketching a right triangle Apply solving a right triangle in real world situations Identify amplitude, frequency, and period in order to write the equations of simple harmonic motion Solve simple harmonic motion problems