EngageNY
Exploiting the Connection to Trigonometry 1
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex number. Groups...
Curated OER
Operations of Complex Numbers and Intro to DeMoivre's Theorem
Students solve problems with complex numbers. For this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.
EngageNY
Roots of Unity
Visualize the nth roots of unity. Pupils calculate the nth roots of unity and find all n roots. Learners plot the solutions in the complex plane and observe that they are the vertices of a regular n-gon inscribed in the unit circle....
EngageNY
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...
EngageNY
Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
Curated OER
Precalculus Exam
In this precalc lesson, learners write out definitions, identify functions, solve integrals and derivatives and graph trig functions as they relate to angles. This is a final exam for precalculus. There are 80 questions on this exam.
EngageNY
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...
Curated OER
Precalculus Pretest
Students complete a pretest as practice for their review. For this precalculus lesson, students find the distance between points and the trigonometric identity of the sine, cosine and tangent. They solve problems using complex and...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
EngageNY
Mid-Module 3 Assessment Task
Time to take a pulse check. The mid-module assessment allows pupils to check where their knowledge falls for the first portion of the module. The 10th resource in a series of 23 covers content from the binomial theorem to hyperbolas....
Curated OER
The Number System
Review complex numbers, real numbers, irrational and rational numbers, integers, and whole numbers with math students. Use this guide as a reference sheet or handout.
EngageNY
Coordinates of Points in Space
Combine vectors and matrices to describe transformations in space. Class members create visual representations of the addition of ordered pairs to discover the resulting parallelogram. They also examine the graphical representation of...
Curated OER
More of DeMoivre's Theorem
Students identify DeMoivre's Theorem. In this precalculus lesson, students derive the law of sine and cosine as it relates to DeMoivre's Theorem. They identify the best time to use these formulas.
Curated OER
Law of Sines and Cosines
Students solve problems using sine and cosine. In this precalculus lesson, students apply the properties of sine and cosine to solve non-right triangle problems. They use Heron's Law to find the area of a shape.
Curated OER
Sine and Cosine
Students solve problems using sine and cosine. In this precalculus lesson, students solve word problems using sine and cosine. They identify where it is appropriate to laws of sine and cosine and where to use the Pythagorean Theorem.
Curated OER
PreCalculus Worksheet 8.4
In this precalculus instructional activity, students write numbers in their trigonometric form and compute the numbers to a given power. Students explore the parametric function and trace the roots of unity. After completing eight...
EngageNY
Solving General Systems of Linear Equations
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
Curated OER
Quadratic Equations with Complex Coefficients
Students solve and graph quadratic equations. In this algebra activity, students perform basic operation using addition, subtraction, multiplication and division. They compute the quadratic formula.
Curated OER
PreCalculus: Final Examination
In this final examination worksheet, students find the tangent function and sine function. They graph problems on a polar coordinate. Students describe trigonometric properties. This twelve-page worksheet contains 80 problems.
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.
EngageNY
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,...
Curated OER
Graphing at all Levels: It's a Beautiful Thing!
Mixing math and art is done in this lesson by applying graphing knowledge to create a unique piece of art. This lesson varies acording to the graphing knowledge of the artist. First, learners identify and review various types of graphing...
Curated OER
Law of Sines and Law of Cosines
In this Pre-calculus/Trigonometry worksheet, students use the laws of sines and cosines to solve triangles. The four page worksheet contains thirteen problems. Answers are not included.