Curated OER
Identities and Trigonometric Values
Young scholars solve trigonometric equations. In this precalculus instructional activity, students prove trigonometric identities using the Pythagorean Theorem. They apply the addition formulas for sine and cosine to prove different...
Curated OER
Area of a Triangle
Students solve the area of triangles. For this precalculus lesson, students are given two sides of a triangle and asked to calculate the area. They apply the law of sine and the side-angle-side area formula to solve.
Curated OER
Law of Sine and Cosine
Students solve problems using the law of sine and cosine. In this precaclulus lesson, students learn the law of DeMoivre's Theorem and Heron's theorem. They use both theorems to solve problems.
Curated OER
Rose Curve
Arcsine will be better understood and applied through prediction the number of petals on a rose curve using polar equations. Students relate rose curve to siusoidal functions using the Ti navigator.
EngageNY
Complex Number Division 1
Conjugating in the math classroom — and we're not talking verbs! The seventh lesson in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to find the...
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Complex Number Division 2
Individuals learn to divide and conquer complex numbers with a little help from moduli and conjugates. In the second instructional activity on complex number division, the class takes a closer look at the numerator and denominator of the...
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Discovering the Geometric Effect of Complex Multiplication
Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...
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Modeling Video Game Motion with Matrices 1
Video game characters move straight with matrices. The first day of a two-day lesson introduces the class to linear transformations that produce straight line motion. The 23rd part in a 32-part series has pupils determine the...
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Modeling Video Game Motion with Matrices 2
The second day of a two-part lesson on motion introduces the class to circular motion. Pupils learn how to incorporate a time parameter into the rotational matrix transformations they already know. The 24th installment in the 32-part...
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When Can We Reverse a Transformation? 3
When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third instructional activity on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous...
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Matrix Multiplication Is Not Commutative
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
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Matrix Multiplication Is Distributive and Associative
Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous lesson in the series, pupils now test the associative and distributive properties. The...
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Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
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Properties of Trigonometric Functions
Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the lesson connects them...
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Tangent Lines and the Tangent Function
Construct tangent lines and make the connection to tangent functions. An informative instructional activity reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a...
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Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
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Modeling with Inverse Trigonometric Functions 1
Where should I stand to get the best view? Pupils use inverse trigonometric functions to determine the horizontal distance from an object to get the best view. They round out the lesson by interpreting their answers within context.
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Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
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Wishful Thinking—Does Linearity Hold? (Part 2)
Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...
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Which Real Number Functions Define a Linear Transformation?
Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...
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An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
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An Appearance of Complex Numbers 2
Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews the...
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Complex Numbers as Vectors
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
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The Geometric Effect of Some Complex Arithmetic 1
Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into what it...
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