Curriculum / Math / 11th Grade / Unit 7: Trigonometric Identities and Equations / Lesson 4
Math
Unit 7
11th Grade
Lesson 4 of 16
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Lesson Notes
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Find angle measures using inverse trig functions in right triangles.
The core standards covered in this lesson
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.6 — Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
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 are sets of three equations that are equivalent. Find $$x$$ for each set of equations.
Solve the following equations. Write your answers in radians.
$${\mathrm{sin}x={1\over2}}$$
$${\mathrm{cos}^{-1}\left({\sqrt2\over2}\right)=x}$$
$${\mathrm{arcsin}(0.35)=x}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find two values where $${\mathrm{cos}x=-1}$$.
What is $${\mathrm{arccos}(-1)}$$?
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.
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Analyze inverse trigonometric functions graphically.
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
F.TF.B.6F.TF.B.7
F.BF.B.4.DF.IF.C.7.EF.TF.B.6F.TF.B.7
Solve linear trigonometric equations.
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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