Curriculum / Math / 11th Grade / Unit 7: Trigonometric Identities and Equations / Lesson 5
Math
Unit 7
11th Grade
Lesson 5 of 16
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Lesson Notes
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Analyze inverse trigonometric functions graphically.
The core standards covered in this lesson
F.BF.B.4.D — Produce an invertible function from a non-invertible function by restricting the domain.
F.IF.C.7.E — Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.TF.B.6 — Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
F.TF.B.7 — Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
The foundational standards covered in this lesson
G.SRT.C.8 — Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Below is a student's answer (in three steps, left to right) to the following problem:
Graph the inverse of the function $${y=\mathrm{sin}x}$$.
What did the student do in each step?
What did the student do well?
How can the student's answer be improved?
What is the solution to the system of:
$$\left\{\begin{matrix} y=\mathrm{cos}x\\ y=-1 \end{matrix}\right.$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find points of intersection of the following functions:
$${f(x)=2\mathrm{sin}x}$$
$${g(x)={-\sqrt3\over 2}}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Solve linear trigonometric equations.
Topic A: Basic Trigonometric Identities and Equivalent Expressions
Derive and verify trigonometric identities using transformations and equivalence of functions.
Standards
F.TF.C.8
Derive and use the Pythagorean identity to write equivalent expressions.
Verify trigonometric identities using Pythagorean and reciprocal identities.
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Topic B: Solve Trigonometric Equations
Find angle measures using inverse trig functions in right triangles.
F.TF.B.6F.TF.B.7
F.BF.B.4.DF.IF.C.7.EF.TF.B.6F.TF.B.7
F.TF.B.7
Solve linear trigonometric equations using $$u$$-substitution.
Use inverse trigonometric functions to solve contextual problems.
Solve quadratic trigonometric equations.
Solve trigonometric equations using identities.
F.TF.B.7F.TF.C.8
Topic C: Advanced Identities and Solving Trigonometric Equations
Evaluate expressions using sum and difference formulas.
F.TF.C.9
Solve equations and prove identities using sum and difference formulas.
Derive double angle formulas and use them to solve equations and prove identities.
Use trigonometric identities to analyze graphs of functions.
F.TF.C.8F.TF.C.9
Topic D: Applications and Extensions of Trigonometric Functions
Use the Law of Sines to find missing side lengths and angle measures in acute triangles.
G.SRT.D.10
Find missing side lengths and angle measures using the Law of Cosines in acute triangles.
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