Algebra 2 Unit 6 Trigonometric Functions
BY THE END OF THIS UNIT:
CORE CONTENT
Cluster Title: FunctionsStandard F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Concepts and Skills to Master
· Convert radian measure to degree measure
· Convert degree measure to radian measure
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Circumference of a circle
· Degree measure of an angle
· Definition of a central angle
Academic Vocabulary:
intercepted arc, radian, positive and negative angles, coterminal
Suggested Instructional Strategies
· Explain what radian measure is and its relation to the intercepted arc
· Use proportion relating degree measure to radian measure
· Use formulas to convert from degrees to radians and vice-versa
· Explain why there is a need for both measures
Honors students may explore formulas involving area or sector or measure of intercepted arc. / Resources:
· Textbook Correlation: 13.3 Radian Measure
Sample Formative Assessment Tasks
Skill-based task:
What is the degree measure of an angle of -3p/4 radians? What is the radian measure of an angle of 27 degrees? / Problem Task: How can angles be used to describe circular motion? Explain the significance of: 180 degrees in circular motion, negative degree in circular motion, more than 360 degrees. See p.841 in textbook, problems 35 and 45.
CORE CONTENT
Standard F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle
Concepts and Skills to Master
· Complete or Derive the Unit Circle with degrees/radians/points
· Definitions of sine, cosine, tangent, reciprocal functions
· Use the unit circle to find trigonometric values
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Knowledge of angles
· Radius and circle
· Quadrants and points
· 30-60-90 triangle theorem
· 45-45-90 triangle theorems
Academic Vocabulary :
standard position, terminal side, unit circle, sine, cosine, tangent, coterminal angles
Suggested Instructional Strategies
· Place info on 30-60-90 and 45-45-90 in the warm-up
· Have students complete / derive the Unit Circle using both radian and degree measure several times
· Have students memorize trig definitions using x, y, and r.
· Find sin, cosine, tangent and their reciprocals using the Unit Circle with many angles or write all six for every angle noted on the unit circle.
Honors should be able to derive the unit circle and complete a trig chart on angle measures. / Resources
· Textbook Correlation: Sections 13.2
o Chapter 13 Tasks
· EmbeddedMath.com
· The_Unit_Circle[1].docx
· Unit_Circle_Right_Triangles[1].doc
Sample Formative Assessment Tasks
Skill-based task :
Find the exact values of sine, cosine, tangent of each angle in degree measure such as -95, 240, 180 or in radian measure. / Problem Task:
Determine the exact values of the sine, cosine, and tangent of 7200, 6000, and 13800. What relationship do these angles have to other “unit circle” angles?
CORE CONTENT
Cluster Title: FunctionsStandard F-TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Concepts and Skills to Master
· Graph parent functions, y=sin x, y=cos x, y=tan x
· Find amplitude, period, phase shift, vertical shift and midline
· Graph transformation of trigonometric functions
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Understanding of the Unit Circle
· Transformations of regular functions from Unit 1
· Graphing points, domain and range
Academic Vocabulary:
periodic function frequency, cycle, period, amplitude and midline
Suggested Instructional Strategies
· Use 13.1 from text as a quick intro
· Use unit circle to graph parent graphs then move quickly to 13.7 the general formula: y=asinb(x-h)+k
· Describe and graph transformations
· Explore the reciprocal functions using the calculator only
Honors may do graphing by hand with reciprocal functions. / Resources
· Textbook Correlation: 13.1, 13.7, 13.8
· Use 13.4, 13.5, 13.6 if you have extra time
· 13.7 Enrichment Activity
· 13.4 TI Calculator Activity
· Sin-Cos-Tan_Graph_Notes[1].docx
Sample Formative Assessment Tasks
Skill-based task :
What is the graph of y=-3sin 2(x-p/3)-3/2 in the interval from 0 to 2p? Find the amplitude, period, phase shift, vertical shift and the midline. / Problem Task: A rainfall problem in central Florida involving sin transformations being changed to cosine, what will change, what will stay the same on p.873 #43, #47 for reasoning, and p.891 #2 about ocean tides
CORE CONTENT
Cluster Title: FunctionsStandard F-TF.8 Prove the Pythagorean identity sin2 +cos2 =1 and use it to find sin (), cos(), or tan (), given sin (), cos (), or tan (), and the quadrant of the angle.
Concepts and Skills to Master
· Verify a Pythagorean identity, concentrate on sin2 +cos2 =1
· Express a trig function in terms of a second (ex: sin x in terms of cos x)
· Simplify trigonometric expressions
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Pythagorean theorem
· Simplifying expressions involving squares and fractions
· Some factoring such as difference of squares
Academic Vocabulary:
basic identities and the Pythagorean identity
Suggested Instructional Strategies
· Derive the Pythagorean identity from the basic identities or using x, y, r.
· Simplify or verify problems with “easy” expressions first
· Use textbook problems, p.401 41-46 / Resources
· Textbook Correlation: 14 – 1
· Chapter 14 Tasks 1 and 3 from Pearson Success Net
Sample Formative Assessment Tasks
Skill-based task:
· Simplify csc2x (1-cos2x)
· Find sin x , given cos x = 3/5 and x in Quadrant I / Problem Task: p. 901 #58
Glencoe Algebra 2/ blue – p.784 #31 and 32 from Physics
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.