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6.08 Bonus Video: Law of Sines—The Ambiguous Case

Resource ID: SE1210B
Grade Range: 10 - 9
Subject: Math

The Law of Sines can be used to solve for sides and angles of oblique triangles. However, in some cases more than one triangle may satisfy the given conditions. We refer to this as an ambiguous case.

SE Precalculus
8
Chapter 5: Introduction to Trigonometry and Graphs

Grade Range: 10 - 9
Subject: Math

In this chapter, we will explore angle measures and the trigonometric ratios, including graphing and inverses.

SE Precalculus
5
Chapter 7: Sequences and Series

Grade Range: 10 - 9
Subject: Math

In this chapter, we introduce sequences and series, some of their applications, and the Binomial Theorem.

SE Precalculus
3
Chapter 4: Systems of Equations

Grade Range: 10 - 9
Subject: Math

In this chapter, we will explore the methods used to solve systems of equations, and real-world situations involving systems of equations.

SE Precalculus
6
Chapter 2: Polynomial and Rational Functions

Grade Range: 10 - 9
Subject: Math

In this chapter, we will explore beyond linear functions and learn about polynomial and rational functions.

SE Precalculus
8
Chapter 6: Trigonometric Identities and Applications

Grade Range: 10 - 9
Subject: Math

In this chapter, students will learn a robust list of trigonometric identities along with their applications. Students will also be introduced to vectors.

SE Precalculus
7
Chapter 8: Conic Sections, Parametric Equations, and Polar Coordinates

Grade Range: 10 - 9
Subject: Math

In this chapter, we introduce conic sections, parametric equations, and polar coordinates.

SE Precalculus
5
Chapter 1: Introduction to Functions and Graphs

Grade Range: 10 - 9
Subject: Math

In this chapter, students are introduced to lines, functions, and graphs of functions.

SE Precalculus
8
Chapter 3: Exponential and Logarithmic Functions

Grade Range: 10 - 9
Subject: Math

In this chapter, students are introduced to exponential and logarithmic functions. Students will learn about the functions' graphs, how to solve equations involving those functions, and their real-world applications.

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Using Logical Reasoning to Prove Conjectures About Quadrilaterals

Resource ID: GM1L18
Grade Range: 10 - 9
Subject: Math

Given conjectures about quadrilaterals, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

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Using Logical Reasoning to Prove Conjectures about Circles

Resource ID: GM1L19
Grade Range: 10 - 9
Subject: Math

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

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Generalizing Geometric Properties of Ratios in Similar Figures

Resource ID: GM2L3
Grade Range: 10 - 9
Subject: Math

Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.

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Determining Area: Sectors of Circles

Resource ID: GM4L3
Grade Range: 10 - 9
Subject: Math

Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.

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Making Conjectures About Circles and Segments

Resource ID: GM4L16
Grade Range: 10 - 9
Subject: Math

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.

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Determining Area: Regular Polygons and Circles

Resource ID: GM4L1
Grade Range: 10 - 9
Subject: Math

The student will apply the formula for the area of regular polygons to solve problems.

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Making Conjectures About Circles and Angles

Resource ID: GM4L16a
Grade Range: 10 - 9
Subject: Math

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.

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Solving Problems With Similar Figures

Resource ID: GM5L2
Grade Range: 10 - 9
Subject: Math

Given problem situations involving similar figures, the student will use ratios to solve the problems.

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Making and Verifying Conjectures about Three-Dimensional Figures

Resource ID: GM1L11
Grade Range: 10 - 9
Subject: Math

Students will explore volume conjectures and solve problems by applying  the volume formulas to composite figures.

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Constructing and Justifying Statements about Geometric Figures

Resource ID: GM1L12
Grade Range: 10 - 9
Subject: Math

Students will distinguish between undefined terms, definitions, postulates, conjectures, and theorems and investigate patterns to make conjectures about geometric relationships.

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Using Counter Examples to Disprove Statements That Are False

Resource ID: GM1L14
Grade Range: 10 - 9
Subject: Math

Given statements about a geometric relationship, the student will use counter examples to disprove statements that are false.

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