Viewers learn how to present basic proofs and verify identities. Highlights Pythagorean, reciprocal and quotient identities. Fermat’s Last Theorem is briefly discussed as one example of a long standing mathematical puzzle.
Languages: English
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Sum and Difference Identities
A number of methods are used to verify the sum and difference identities. The negative and complementary arc identities are proven, exact values calculated, double angle identities are derived, and equations solved using identities.
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Introduction to Math Factor
This 15-minute video familiarizes viewers with the Math Factor series by presenting examples from programs and demonstrating how to use the video and print components.
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Solving Complex First- and Second-Degree Equations and Relationships
Trigonometric equations are solved using identities, systems of equations, and graphing technology. The cyclical nature of tides is explored.
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Introduction to Polynomial Functions and Their Graphs
Water fountains and speeding cars are used to introduce polynomial functions, the basic terminology, the classification and properties of polynomial functions (domain, range, x- and y- intercepts), as well as rudimentary graphing techniques.
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Trigonometric and Circular Functions Review
A review of trigonometric and circular functions. Topics receiving special attention include radian measure, transformation of trigonometric functions, solving trigonometric equations, and proving identities.
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Division of Polynomial Functions and Their Graphs
Historical anecdotes intersperse the teaching of long division with linear and nonlinear divisors. The concept of synthetic division is also presented, along with a strategy for finding missing coefficients.
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Sketching and Graphing Exponential Functions
Students learn to recognize the general characteristics of the graphs of exponential functions with various bases. Situations involving exponential growth and decay are explored. Students solve and verify exponential equations.
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The Remainder and Factor Theorems
The Remainder Theorem is illustrated, proven, and then used to prove the Factor Theorem.