Trigonometry

Transcription

1 Trigonometry Department: Math Level: Standard Length of Class: Semester Number of Credits: 1 Grades: Prerequisites: Algebra 2 Application Needed: No College credit available: No Credit completion available: Meets graduation requirement: No Course Description: This course is an informal approach to Trigonometry with emphasis on application. Topics include: definition of trig functions, applications with right and oblique triangles, rectangular and polar graphs, identities, inverse functions, trig equations, and complex numbers. Competency 1: Fundamentals of Trigonometry: understand that trigonometry is based on ratios and relationships between angles and sides of triangles. understand that algebraic properties can be used to solve conditional Beyond understanding of the six ratios. knowledge of the 6 ratios to solve problems in increasingly complex situations. knowledge of the 6 ratios to solve problems. I can define and identify the 6 ratios on and off the coordinate plane. incompletely define and identify the 6 ratios on and off the coordinate plane.

2 understanding of angle measure, reference angles and co-terminal angles. knowledge of different angle measure types to solve problems in increasingly complex situations. knowledge of different angle measure types to solve problems. I can convert angles between degrees, radians, and revolutions. AND I can calculate and locate reference and coterminal angles. incompletely convert angles between degrees, radians and revolutions. OR I can calculate and locate reference and coterminal angles with errors. understanding of the inverse functions. knowledge of inverse functions to solve real world problems. knowledge of inverse functions to solve problems on and off the coordinate plane. I can use the definition of inverse functions to identify an angle given a ratio with and without a calculator. I can use the definition of inverse functions to identify an angle incorrectly given a ratio with and without a calculator. understanding of how to solve problems involving triangles. knowledge of triangles to solve real world problems. I can find all sides and angles of both triangles for the ambiguous case. I can determine how many triangles exist for a given set of conditions. AND If exactly one triangle exists, I can solve the triangle for all sides and angles and area. I can inconsistently determine how many triangles exist for a given set of conditions. OR If exactly one triangle exists, I can solve the triangle for all sides and angles and area with errors. I can model or solve real I can find the solution I can find the solution I can inconsistently or

3 to solve conditional world problems by determining an appropriate solution set. set of angles for more complex set of angles for basic incorrectly find the solution set of angles for basic Competency 2: Graphing and Trigonometric Models: understand that functions are periodic and can be modeled in various ways. Beyond to graph functions. I can create and use a mathematical model based on a real world situation or graph. I can identify the key characteristics and graph more complex functions. I can identify the key characteristics and graph the 6 functions. inconsistently identify the key characteristics and graph the 6 functions.

4 Competency 3: Identities: understand that identities are special types of equations that are used to verify/prove the equivalence of I can synthesize expressions and algebraic manipulations into a specific form. Beyond I can transform a expression into a specific form. I can inconsistently or incorrectly recall to simplify, transform, and evaluate to evaluate and symbolically manipulate I can recall to simplify, transform, and evaluate to justify an identity through symbolically manipulating I can synthesize and more complex algebraic manipulations to prove an identity. I can prove an identity with algebraic manipulations. I can recognize when an equation is an identity and recall the appropriate to show a relationship to be true. I can inconsistently or incorrectly recognize when an equation is an identity and recall the appropriate to show a relationship to be true.

5 Competency 6: Fact Fluency: to quickly and accurately verbalize and compute fact fluency. (s) be able to demonstrate the ability to accurately and efficiently perform basic mathematical skills, procedures, and recall necessary facts as determined by course. I can demonstrate fluency with course determined skills, procedures, and necessary facts. I can inconsistently demonstrate fluency with course determined skills, procedures, or necessary facts.