Mathematics Curriculum
  Trigonometry
 

Trigonometry topics include circular functions, right triangle ratios, solutions of trigonometric equations, inverses, identities, the laws of sines and cosines, graphs of trigonometric functions, and applications of trigonometric techniques to solve real-world problems. A transformational approach to graphing is used with families of related graphs. Numerical, graphical, and algebraic solutions should be considered for all problems where appropriate. Graphing utilities, especially graphing calculators, are integral to the course.

Last Updated: 09/08/11 10:13 AM
 
 
MTH.T
Standard 1
  CONNECT CIRCULAR FUNCTION WITH TRIG FUNCTION DEFINITIONS
 

Benchmark 1.a
Connect Circular Function with Trig Function Definitions
 
Indicator 1.a.1
Define the six triangular trigonometric functions of an angle
 
Indicator 1.a.2
Define the six circular trigonometric functions of an angle
 
Indicator 1.a.3
Make connection between triangular/circular trig functions
 
Indicator 1.a.4
Recognize and draw an angle in standard position
 
Indicator 1.a.5
Determine a triangle from a point on the terminal side of an angle
 
Indicator 1.a.6
Find angles that are coterminal with a given angle
 
MTH.T
Standard 2
  FIND THE VALUES OF TRIG FUNCTIONS AND RELATE TO THE UNIT CIRCLE
 

Benchmark 2.a
Given The Value of One Trig Function, Find Remaining Trig Values
 
Indicator 2.a.1
Find all related trig function values, given the value of one
 
Indicator 2.a.2
Develop the unit circle, using both degrees and radians
 
Indicator 2.a.3
Use circular function definitions and unit circle to solve problems
 
Indicator 2.a.4
Make connections between unit circle and coordinate geometry
 
Indicator 2.a.5
Make connections between unit circle & cosine/sine values
 
Indicator 2.a.6
Make connections between unit circle & special right triangles
 
MTH.T
Standard 3
  FIND EXACT TRIG VALUES OF SPECIAL ANGLES IN DEGREES AND RADIANS
 

Benchmark 3.a
Find Trig Values of Special Angles Without A Calculator
 
Indicator 3.a.1
Find trig function values of special angles in degrees and radians
 
Indicator 3.a.2
Apply the properties of the unit circle without using a calculator
 
Indicator 3.a.3
Convert from radians to degrees and from degrees to radians
 
MTH.T
Standard 4
  APPROXIMATE VALUES OF TRIG FUNCTIONS AND INVERSE TRIG FUNCTIONS
 

Benchmark 4.a
Use A Calculator To Approximate Trig Values and Inverse Trig Values
 
Indicator 4.a.1
Use a calculator to approximate trig values in degrees and radians
 
Indicator 4.a.2
Define inverse trigonometric functions
 
Indicator 4.a.3
Use inverse trig functions to find angle measures
 
MTH.T
Standard 7
  IDENTIFY THE DOMAIN, RANGE, AND GRAPHS OF INVERSE TRIG FUNCTIONS
 

Benchmark 7.a
Identify The Domain, Range, And Graphs Of Inverse Trig Functions
 
Indicator 7.a.1
Find the domain and range of inverse trig functions
 
Indicator 7.a.2
Find the values of inverse trig functions
 
Indicator 7.a.3
Identify the graphs of inverse trig functions
 
Indicator 7.a.4
Graph inverse trig functions using transformations
 
Indicator 7.a.5
Evaluate expressions of composite trig and inverse trig functions
 
MTH.T
Standard 5
  VERIFY BASIC TRIGONOMETRIC IDENTITIES
 

Benchmark 5.a
Verify Basic Trig Identities Using Substitution
 
Indicator 5.a.1
Verify trig identities using reciprocal and Pythagorean identities
 
Indicator 5.a.2
Verify trig identities using sum and difference identities
 
Indicator 5.a.3
Verify trig identities using double-angle identities
 
Indicator 5.a.4
Verify trig identities using quotient identities
 
MTH.T
Standard 6
  FIND DOMAIN, RANGE, AMPLITUDE, PERIOD AND GRAPH TRIG FUNCTIONS
 

Benchmark 6.a
Determine The Domain And Range Of Trig Functions
 
Indicator 6.a.1
State the domain and range of trig functions
 

Benchmark 6.b
Determine The Amplitude, Period, Phase Shift, And Vertical Shift
 
Indicator 6.b.1
Determine the amplitude, period, phase shift, and vertical shift
 
Indicator 6.b.2
Describe the effects of changing parameters in a trig equation
 
Indicator 6.b.3
Write equations of trig functions
 
Indicator 6.b.4
Determine and graph trig functions from real-world situations
 

Benchmark 6.c
Sketch The Graph Of A Trig Function Using Transformations
 
Indicator 6.c.1
Sketch the graph of a trig function for at least one period or cycle
 
Indicator 6.c.2
Sketch the graphs of the six trig functions using transformations
 
MTH.T
Standard 8
  SOLVE TRIG EQUATIONS AND INEQUALITIES
 

Benchmark 8.a
Solve Trig Equations With Infinite Solutions and Restricted Domains
 
Indicator 8.a.1
Solve trig equations with restricted domains
 
Indicator 8.a.2
Solve trig equations with infinite solutions
 
Indicator 8.a.3
Verify algebraic solutions and check reasonableness
 
MTH.T
Standard 9
  SOLVE PRACTICAL PROBLEMS USING THE LAW OF SINES AND COSINES
 

Benchmark 9.a
Use The Pythagorean Theorem, The Law Of Sines, And The Law Of Cosines
 
Indicator 9.a.1
Create a practical problem involving triangles
 
Indicator 9.a.2
Solve a practical problem involving triangles
 
Indicator 9.a.3
Solve problems using law of sines, cosines, and pythagorean theorem
 
Indicator 9.a.4
Identify a solution technique that could be used with a given problem
 
Indicator 9.a.5
Find the area of triangles using Heron's formula and the sine formula
 
MTH.T
Standard 10
  PERFORM OPERATIONS ON VECTORS AND SOLVE PRACTICAL PROBLEMS
 

Benchmark 10.a
Perform Operations On Vectors And Solve Practical Problems
 
Indicator 10.a.1
Use vector notation
 
Indicator 10.a.2
Perform operations on vectors
 
Indicator 10.a.3
Graph vectors and resultant vectors
 
Indicator 10.a.4
(Optional) Express complex numbers in vector notation
 
Indicator 10.a.5
Define unit vector and find unit vectors
 
Indicator 10.a.6
Perform vector addition, scalar multiplication and find dot products
 
Indicator 10.a.7
Find vector components
 
Indicator 10.a.8
Find the norm of a vector
 
Indicator 10.a.9
Use vectors in geometric proofs
 
Indicator 10.a.10
(Optional) Perform operations with vectors in space


Essential - Standard, benchmark, or indicator from the VDOE Standards of Learning document. In the absence of VDOE standards for a given course, content subject to testing such as AP and IB can be labeled Essential.
Expected - Standard, benchmark, or indicator added by the FCPS Program of Studies to provide a context, a bridge, or an enhancement to the Essential SBIs.
Extended - Standard, benchmark, or indicator added by the FCPS Program of Studies generally used to differentiate instruction for advanced learners (Honors/GT)