Students expand on their knowledge of trigonometry, developing a foundation for calculus concepts by expanding their conception of trigonometric functions and looking at connections between functions.
Math
Unit 7
11th Grade
Unit 7, Trigonometric Identities and Equations, builds on the previous unit on trigonometric functions to expand students’ knowledge of trigonometry. Students develop a foundation for calculus concepts by expanding their conception of trigonometric functions and looking at connections between trigonometric functions. Reasoning flexibly about trigonometric functions and seeing that expressions that look different on the surface can actually act the same on certain domains sets the stage for a study of differentiation and integration, where periodic functions have many useful properties and act as useful tools to study calculus.
Students also apply algebraic techniques to trigonometry. This part of the unit reinforces algebraic skills while also helping students to better understand trigonometric functions graphically and through the unit circle. As students move more flexibly between representations of trigonometric functions, they develop skills in seeing structure in those functions and practice looking at mathematical objects from multiple perspectives and bringing prior knowledge to bear on a new context. This type of relational thinking helps students to see the power of algebraic manipulation and structure in expressions, allowing them to work more flexibly and to see connections more readily.
Pacing: 18 instructional days (16 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Identity | Pythagorean identity |
Cofunction identities | Inverse trig functions (arcsin, arccos, arctan, arcsec, arccsc, arccot) |
Reciprocal identities | $${\mathrm{sin}^{-1}x}$$ notation for inverse trig functions |
Negative angle identities | Linear trigonometric equations |
$$u$$-substitution | Quadratic trigonometric equations |
General solution | Exact solution |
Double angle formula | Sum formula |
Difference formula | Law of Cosines |
Law of Sines |
Topic A: Basic Trigonometric Identities and Equivalent Expressions
Topic B: Solve Trigonometric Equations
Topic C: Advanced Identities and Solving Trigonometric Equations
Topic D: Applications and Extensions of Trigonometric Functions
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 6
Unit Circle and Trigonometric Functions
Unit 8
Probability and Statistical Inference