Download Trigonometry - DocuShare - Pleasant Valley School District

PLEASANT VALLEY SCHOOL DISTRICT
PLANNED COURSE CURRICULUM GUIDE
TRIGONOMETRY - HIGHER LEARNING
GRADES 11 AND 12
I.
COURSE DESCRIPTION AND INTENT:
Trigonometry is a course designed as one of the essential underpinnings for advanced
courses in mathematics. This course includes an initial study of circular functions,
fundamental identities, vectors, trigonometric equations, solution of triangles,
matrices and complex numbers.
II.
INSTRUCTIONAL TIME:
Class Periods: 6 per 6-day cycle
Length of Class Periods (minutes): 56
Length of Course: 90 days
Unit of Credit: .5
Updated: June, 2014
COURSE: Trigonometry
STRAND: 2.3.HS. (Geometry)
GRADE(S): 11 and 12
TIME FRAME: One Semester
PA CORE STANDARDS
CC.2.3.HS.A.7 – Apply trigonometric ratios to solve problems involving right triangles.
CC.2.3.8.A.3 – Understand and apply the Pythagorean Theorem to solve problems.
ASSESSMENT ANCHORS
Intentionally Blank
RESOURCES















Textbook: Trigonometry, 2nd ed. – by Dugopolski
Teacher designed materials
OBJECTIVES
The learner will use the definitions of the six trigonometric functions to solve right
triangle problems.
The learner will use the Law of Sines or the Law of Cosines to solve an oblique
triangle.
ESSENTIAL CONTENT
Name arcs and angles in degrees.
Identify angles in standard position.
Define and identify coterminal angles.
Based upon the fractional part of a circle find the length of a given arc.
Establish the trigonometric ratios of sine, cosine, tangent, cotangent, secant, and
cosecant in terms of right triangle relationships.
Calculate the values of the trigonometric ratios of specific angles.
Use the idea of a circle in standard position and extend the ideas of trigonometric
ratios to any angle.
Define reference angle.
Find the reference angle (triangle) for any angle.
Use the techniques of geometry for equilateral triangles and isosceles right triangles
to find the values of "special" angles - i.e. 30, 45, 60, 90.
Use the co-function relationships to calculate the values of the trigonometric ratios of
complementary angles.





Apply trigonometric ratios to the solution of right triangles, using where possible
practical problems.
Review the right triangle relationships of the trigonometric ratios.
Apply the solution of right triangles to physical problems.
Define the Law of Sines.
Define the Law of Cosines.



INSTRUCTIONAL STRATEGIES
Jigsaw learning activity to establish the six trigonometric ratios.
Use mnemonic devices such as SOH-CAH-TOA and all students take calculus to help
students to remember basic trigonometry facts.
Use string, pencil, and ruler to mark off radians on a circle.
Inner-outer circle activity to practice calculating trigonometric ratios.
Use a ruler, pencil and protractor to construct possible solutions for triangles.







ASSESSMENTS
Teacher designed tests and quizzes
Activities which demonstrate knowledge of the concepts taught
Worksheets designed to demonstrate knowledge of the concepts taught
Portfolio assessment
Written or oral presentation of projects
Homework assessment
Cooperative group assessment


CORRECTIVES/EXTENSIONS
Correctives:
 Utilize re-teaching activities.
 Individualized instruction via the classroom teacher or math tutoring lab.
Extensions:
 Outdoor, sunny day activity: measure shadows to find the angle of elevation of
the sun.
 Collaborate with physics teacher/class on applications of Laws of Sines and
Cosines (i.e. vectors, surveying, etc.)

COURSE: Trigonometry
STRAND: 2.2.HS. (Algebraic Concepts)
GRADE(S): 11 and 12
TIME FRAME: One Semester
PA CORE STANDARDS
CC.2.2.HS.C.2 – Graph and analyze functions and use their properties to make
connections between the different representations.
CC.2.2.HS.C.7 – Apply radian measures of an angle and the unit circle to analyze the
trigonometric functions.
CC.2.2.HS.C.8 – Choose trigonometric functions to model periodic phenomena and
describe the properties of the graph.
CC.2.2.HS.D.9 – Use reasoning to solve equations and justify the solution method.
ASSESSMENT ANCHORS
RESOURCES
Textbook: Trigonometry, 2nd ed. – by Dugopolski
Teacher designed materials







OBJECTIVES
The learner will construct the graphs of the six trigonometric functions.
The learner will use the fundamental trigonometric identities to simplify
expressions and verify identities.
The learner will solve trigonometric equations.
ESSENTIAL CONTENT
Deduce a method to name angles in radians.
Convert degree measures for angles into radians and vice-versa.
Use radians to calculate the length of an arc.
Graph the functions - sine x, cosine x, tangent x, cotangent x, secant x, and cosecant





























x, in the coordinate plane.
Define amplitude.
Make changes in the amplitude of sine and cosine graphs.
Define period - when used in relation to graphing.
Make changes of period to the graphs of sine, cosine, tangent, cotangent, secant and
cosecant functions.
Define Phase Displacement of Phase Shift.
Make displacements of graphs noting right or left movements.
Given the graph of a trigonometric function, write its equation.
Establish the Reciprocal Identities, the Quotient Identities, the Pythagorean Identities,
and the Negative-Angle Identities.
Use the above-mentioned identities and simplify other trigonometric expressions.
Use the above-mentioned identities and also prove other equations to be identities.
Establish the Sum-and-Difference-of-Angles Identities.
Use these identities to prove other identities.
Solve trigonometric equations.
Solve equations involving trigonometry taken from other sciences.
Form the inverses of trigonometric functions giving special attention to the
restrictions of the domain necessary to maintain function status.
Simplify expressions involving inverses of trigonometric functions.
Solve equations involving inverse of trigonometric functions.
INSTRUCTIONAL STRATEGIES
Use a graphing calculator to discover the effects that variables have on the basic sine
curve.
Jigsaw learning activity to graph the six trigonometric functions.
Cooperative group activity to establish the effects that the parameters have on the
trigonometric functions.
Use flashcards to assist students in memorizing the trigonometric identities.
Use the "sine-cosine song" to assist students in memorizing the sum and difference
formulas.
ASSESSMENTS
Teacher designed tests and quizzes
Activities which demonstrate knowledge of the concepts taught
Worksheets designed to demonstrate knowledge of the concepts taught
Portfolio assessment
Written or oral presentation of projects
Homework assessment
Cooperative group assessment
CORRECTIVES/EXTENSIONS
Correctives:
 Utilize re-teaching activities.
 Individualized instruction via the classroom teacher or math tutoring lab.
Extensions:
 Create designs using the graphs of the trigonometric functions for display in the
hallways of the school.
 Project: "You Be the Teacher" -Students must explain in written form how to
simplify a trigonometric expression.
 Students write their own word problems that involve trigonometric equations, solve
them, then give them to another student to solve.