mvsd
Math Curriculum 01/12/03

Mathematics - Trigonometry

Mathematics

The Idaho State Achievement Standards for Mathematics provides skills for kindergarten through twelfth grade.

Trigonometry

The Indiana Trigonometry course "has its origins in the study of triangle measurement. Natural generalizations of the ratios of right-triangle trigonometry give rise to both trigonometric and circular functions. These functions, especially the sine and cosine, are mathematical models for many periodic real world phenomena. Students studying trigonometry should explore data from such real world phenomena, but should also identify and analyze the corresponding trigonometric models. The study of inverse trig functions; trig equations and identities; the Law of Sines and the Law of Cosines; vectors; and polar coordinates should also be included in the course.

Scientific calculators and graphing technology play an important role in the development of students' understanding of the concepts of trigonometry as well as providing students with more time and power to explore realistic applications.

It is important to note that all of the objectives and competencies listed in this outline have also been included in the list of competencies for Pre-Calculus."


Algebraic Concepts

    Solve Equations
The learner will be able to solve given equations.
Strand Bloom's Scope Hours Source
Solve Equations Master 1.0 ID: State Achievement Standards, 2001, Grades 9-12, 305.03; ISAT
  

Calculus and Pre-Calculus

    Vectors: Representing
The learner will be able to develop and apply an understanding of vectors in representing direction and magnitude, as well as with operations.
Strand Bloom's Scope Hours Source
Vectors Application Master ID: State Achievement Standards, 2001, Grades 9-12, 351.03b
  
    Complex Numbers :Trigonometric Form
The learner will be able to show complex numbers in trigonometric form.
Strand Bloom's Scope Hours Source
Complex Numbers Application Master 1.0 District Expectation
  
    Vectors: Define
The learner will be able to define a vector.
Strand Bloom's Scope Hours Source
Vectors Knowledge Master 0.5 ID: State Achievement Standards, 2001, Grades 9-12, 351.03.b
  
    Vectors: Linear Equa
The learner will be able to represent lines as vector equations.
Strand Bloom's Scope Hours Source
Vectors Application Master 0.5 District Expectation
  
    Vectors: Real World Problems
The learner will be able to solve real world problems using vectors.
Strand Bloom's Scope Hours Source
Vectors Application Master 1.0 ID: State Achievement Standards, 2001, Grades 9-12, 351.03.b
  

Functions

    Trigonometric Functions
The learner will be able to understand and apply trigonometric functions and how they are used.
Strand Bloom's Scope Hours Source
Trigonometric Functions Master ID: State Achievement Standards, 2001, Grades 9-12, 353.01
  
    Trig. Functions: Inverse/Define/Evaluate
The learner will be able to define the inverse of a trigonometric function.
Strand Bloom's Scope Hours Source
Trigonometric Functions Application Master 0.5 ID: State Achievement Standards, 2001, Grades 9-12, 353.01
  
    Trigonometric Functions: Graphing
The learner will be able to graph trigonometric functions.
Strand Bloom's Scope Hours Source
Trigonometric Functions Master 1.0 District Expectation
  
    Trig Functions: Attributes/Graphing
The learner will be able to determine the following attributes for trigonometric functions: domain, range, period, amplitude, intercepts, and asymptotes.
Strand Bloom's Scope Hours Source
Trigonometric Functions Application Master 1.0 District Expectation
  
    Trig. Functions: Translation/Graph/Analy
The learner will be able to graph and/or analyze the translation of a given trigonometric function.
Strand Bloom's Scope Hours Source
Trigonometric Functions Analysis Master 1.0 District Expectation
  
    Trigonometric Functions: Application
The learner will be able to apply trigonometric functions in real world scenarios.
Strand Bloom's Scope Hours Source
Trigonometric Functions Application Master 1.5 ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a
  
    Trigonometric Functions: Graph/Analyze
The learner will be able to analyze the graphs of trigonometric functions.
Strand Bloom's Scope Hours Source
Trigonometric Functions Analysis Master 1.0 ID: State Achievement Standards, 2001, Grades 9-12, 353.02.a; ISAT
  
    Graphing: Functions/Relations
The learner will be able to graph relations and functions using technology.
Strand Bloom's Scope Hours Source
Graphing Functions Application Master 1.0 ID: State Achievement Standards, 2001, Grades 9-12, 352.05.a
  
    Functions: Analyzing
The learner will be able to analyze functions by determining such characteristics as their domain, range, asymptotes, and zeros.
Strand Bloom's Scope Hours Source
Functions Analysis Master 1.0 District Expectation
  

Technology

    Technology as a Tool: Scientific/Graphs
The learner will be able to become adept at using scientific calculators and graphing technology.
Strand Bloom's Scope Hours Source
Technology as a Tool Master ID: State Achievement Standards, 2001, Grades 9-12, 348.03
  

Trigonometry

    Triangles: Solving Right
The learner will be able to find the measure of each unknown side (to the nearest tenth or hundredth) or angle (to the nearest degree), solve real world trigonometry problems, and include the angle of depression or elevation in calculations.
Strand Bloom's Scope Hours Source
Triangles Comprehension Master ID: State Achievement Standards, 2001, Grades 9-12, 351.02a; 351.02.b
  
    Connecting: Trig./Polar/Complex
The learner will be able to make connections among trigonometric functions, polar coordinates, and complex numbers.
Strand Bloom's Scope Hours Source
Connecting Master District Expectation
  
    Connecting: Triangle/Trig./Circular
The learner will be able to make connections between concepts of ratios within right triangles, the trigonometric functions, and circular functions.
Strand Bloom's Scope Hours Source
Connecting Master ID: State Achievement Standards, 2001, Grades 9-12, 351.02
  
    Trig. Identities
The learner will be able to identify and use the trigonometric identities.
Strand Bloom's Scope Hours Source
Trigonometric Identities Master District Expectation
  
    Problem Solving: Trigonometry
The learner will be able to solve a variety of real world problems by applying both technology and trigonometric concepts.
Strand Bloom's Scope Hours Source
Problem Solving Application Master ID: State Achievement Standards, 2001, Grades 9-12, 351.02.b
  
    Trig. Ratios: Identify Specific Values
The learner will be able to identify the trigonometric values of sine, cosine, and tangent for the following angles and their multiples: 0, 30, 45, 60, 90, and 180.
Strand Bloom's Scope Hours Source
Trigonometric Ratios Knowledge Master 0.5 ID: State Achievement Standards, 2001, Grades 9-12, 351.02.b; ISAT
  
    Trig. Ratios: Define/Unit Vector
The learner will be able to define the trigonometric terms sine, cosine, tangent, secant, cosecant, and cotangent using the ordered pair on a given unit vector.
Strand Bloom's Scope Hours Source
Trigonometric Ratios Knowledge Master 1.0 ID: State Achievement Standards, 2001, Grades 9-12, 351.02.b
  
    Trig. Ratios: Law of Sines/Cosines
The learner will be able to use the Law of Sines and Cosines to solve problems.
Strand Bloom's Scope Hours Source
Trigonometric Ratios Application Master 1.5 ID: State Achievement Standards, 2001, Grades 9-12, ; ISAT
  
    Connecting: Across Forms
The learner will be able to solve a given problem for the appropriate trigonometric ratios, radian measures, and angle measures.
Strand Bloom's Scope Hours Source
Connecting Application Master 1.0 District Expectation
  
    Trig. Identities: Verifying
The learner will be able to verify the trigonometric identities.
Strand Bloom's Scope Hours Source
Trigonometric Identities Application Master 1.0 District Expectation
  
    Trig. Expressions: Evaluate
The learner will be able to evaluate trigonometric expressions.
Strand Bloom's Scope Hours Source
Trigonometric Equations Application Master 1.0 ID: State Achievement Standards, 2001, Grades 9-12, 350.02.a; ISAT
  
    Trig. Expressions: Evaluate
The learner will be able to evaluate inverse trigonometric expressions.
Strand Bloom's Scope Hours Source
Trigonometric Equations Application Master 1.0 District Expectation
  
    Trig. Equations: Solving
The learner will be able to calculate solutions for trigonometric equations.
Strand Bloom's Scope Hours Source
Trigonometric Equations Application Master 2.0 District Expectation
  
    Trig. Equations: Determine From Problem
The learner will be able to write a trigonometric equation which most appropriately represents a given real world situation.
Strand Bloom's Scope Hours Source
Trigonometric Equations Application Master 0.5 District Expectation
  
    Angle Measure: Converting
The learner will be able to convert between degree and radian measure.
Strand Bloom's Scope Hours Source
Radians/Angles Synthesis Master 1.0 District Expectation
  
    Polar Coordinates: Define
The learner will be able to give a definition of polar coordinates.
Strand Bloom's Scope Hours Source
Polar Forms/Equations/Graphs Knowledge Master 0.5 District Expectation
  
    Polar Equations: Graph
The learner will be able to represent polar equations in graphical form.
Strand Bloom's Scope Hours Source
Polar Forms/Equations/Graphs Application Master 1.0 District Expectation
  
    Polar Form: Transfer to Cartesian
The learner will be able to convert between cartesian and polar coordinates.
Strand Bloom's Scope Hours Source
Polar Forms/Equations/Graphs Synthesis Master 1.0 District Expectation
  

© 2004 by mvsd and EdVISION Corporation.  All Rights Reserved. Made with Curriculum Designer by EdVISION Corporation.