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6.08 Bonus Video: Law of Sines—The Ambiguous Case
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.
8 Chapter 5: Introduction to Trigonometry and Graphs
In this chapter, we will explore angle measures and the trigonometric ratios, including graphing and inverses.
5 Chapter 7: Sequences and Series
In this chapter, we introduce sequences and series, some of their applications, and the Binomial Theorem.
3 Chapter 4: Systems of Equations
In this chapter, we will explore the methods used to solve systems of equations, and real-world situations involving systems of equations.
6 Chapter 2: Polynomial and Rational Functions
In this chapter, we will explore beyond linear functions and learn about polynomial and rational functions.
8 Chapter 6: Trigonometric Identities and Applications
In this chapter, students will learn a robust list of trigonometric identities along with their applications. Students will also be introduced to vectors.
7 Chapter 8: Conic Sections, Parametric Equations, and Polar Coordinates
In this chapter, we introduce conic sections, parametric equations, and polar coordinates.
5 Chapter 1: Introduction to Functions and Graphs
In this chapter, students are introduced to lines, functions, and graphs of functions.
8 Chapter 3: Exponential and Logarithmic Functions
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.
6 OnTRACK Algebra I: Properties and Attributes of Functions
Students will learn how to use the properties and attributes of functions.
Solving Quadratic Equations Using Algebraic Methods
Given a quadratic equation, the student will solve the equation by factoring, completing the square, or by using the quadratic formula.
Quadratics: Connecting Roots, Zeros, and x-Intercepts
Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.
Using the Laws of Exponents to Solve Problems
Given problem situations involving exponents, the student will use the laws of exponents to solve the problems.
Formulating Systems of Equations (Verbal → Symbolic)
Given verbal descriptions of situations involving systems of linear equations the student will analyze the situations and formulate systems of equations in two unknowns to solve problems.
Solving Quadratic Equations Using Graphs
Given a quadratic equation, the student will use graphical methods to solve the equation.
Determining the Meaning of Intercepts
Given algebraic, tabular, and graphical representations of linear functions, the student will determine the intercepts of the function and interpret the meaning of intercepts within the context of the situation.
Predicting the Effects of Changing y-Intercepts in Problem Situations
Given verbal, symbolic, numerical, or graphical representations of problem situations, the student will interpret and predict the effects of changing the y-intercept in the context of the situations.
Solving Linear Inequalities
The student will represent linear inequalities using equations, tables, and graphs. The student will solve linear inequalities using graphs or properties of equality, and determine whether or not a given point is a solution to a linear inequality.
Direct Variation and Proportional Change
The student will use a variety of methods inculding tables, equations and graphs to find the constant of variation and missing values when given a relationship that varies directly.