﻿ FCPS Program of Studies
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)