Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.
This tasks examines how to calculate the area of an equilateral triangle using high school geometry.
This task complements ``Seven Circles'' I, II, and III. This is a hands-on activity which students could work on at many different levels and the activity leads to many interesting questions for further investigation.
This task provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. When the task is complete, new insight is shed on the ``Seven Circles I'' problem which initiated this investigation as is noted at the end of the solution.
This task is closely related to very important material about similarity and ratios in geometry.
The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.
This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.
Precalculus 1 & 2 / Trigonometry provides a study of functions and their graphs, including polynomial, rational, exponential, and logarithmic functions. Additionally, right-triangle trigonometry, trigonometric functions and their applications are covered.
This course begins by establishing the definitions of the basic trig functions and exploring their properties, and then proceeds to use the basic definitions of the functions to study the properties of their graphs, including domain and range, and to define the inverses of these functions and establish the their properties. Through the language of transformation, the student will explore the ideas of period and amplitude and learn how these graphical differences relate to algebraic changes in the function formulas. The student will also learn to solve equations, prove identities using the trig functions, and study several applications of these functions. Upon successful completion of this course, the student will be able to: measure angles in degrees and radians, and relate them to arc length; solve problems involving right triangles and unit circles using the definitions of the trigonometric functions; solve problems involving non-right triangles; relate the equation of a trigonometric function to its graph; solve trigonometric equations using inverse trig functions; prove trigonometric identities; solve trig equations involving identities; relate coordinates and equations in Polar form to coordinates and equations in Cartesian form; perform operations with vectors and use them to solve problems; relate equations and graphs in Parametric form to equations and graphs in Cartesian form; link graphical, numeric, and symbolic approaches when interpreting situations and analyzing problems; write clear, correct, and complete solutions to mathematical problems using proper mathematical notation and appropriate language; communicate the difference between an exact and an approximate solution and determine which is more appropriate for a given problem. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 003)
This course will cover families of trigonometric functions, their inverses, properties, graphs, and applications. Additionally we will study trigonometric equations and identities, the laws of sines and cosines, polar coordinates and graphs, parametric equations and elementary vector operations.Login: guest_oclPassword: ocl
Precalculus (was College Algebra) is an introductory text. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. Note: this book was updated on the BC Open textbook Project site on February, 17, 2015 to include the version of the textbook with chapters on Trigonometry.
This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.
In this lesson, students will summarize the understanding of trigonometric functions by model periodic phenomena with specified amplitude, frequency, and midline through storytelling.