Brief Descriptions of Math 25 Units

For details, use the link for the unit number below (left column).
Unit Brief Description
1 Angles; Trigonometric Functions defined using Right Triangles
  • Unit 1 begins with a discussion of angles and various ways to measure angles: radians, decimal degrees, and degrees-minutes-seconds.You are probably familiar with degrees, but in mathematics it is more convenient to use radians. You will also learn to convert between the three measurements.
  • The six trigonometric functions are then defined in terms of right triangles (in Unit 2, you will learn a second approach to the definition in terms of the unit circle). You will also learn how to compute the exact values of these functions at certain angles, and approximations at more general angles. It is Math Department policy that students should be able to compute the exact values of all the circular (trigonometric) functions at the "standard" angles, i.e., all multiples of pi/6 and pi/4 radians and 30 and 45 degrees.
  • Finally, you will also learn some of the basic identities that are satisfied by the trigonometric functions.
    • 2 Trigonometric functions generalized beyond right triangles; applications involving right triangles
  • The first part of Unit 2 continues the development of the trigonometric functions by studying their values at general angles. First, these values are computed by using the reference triangle technique. Then an alternative approach, using the unit circle, is given. In fact, this actually provides a second alternative definition of the trigonometric functions. It is very important that you learn both approaches to the definition and calculation of trigonometric functions.
  • In the second part of Unit 2, you will see how trigonometry can be used to solve a large variety of applications involving right triangles.
    • 3 Graphs of Sine and Cosine Functions; Simple Harmonic Motion
    In this unit, you will study the basic properties of the graphs of the sine and cosine functions, with variations. You will also apply your knowledge of these to various spring problems.
    4 Graphs of all Trigonometric Functions; Graphs of some Inverse functions
    In this unit, you will study the graphs of tangent, cotangent, secant, and cosecant, with variations. You will also study the inverse trigonometric functions. The textbook is quite brief in these three sections, so supplementary material and exercises is included.
    5 Fundamental Trignometric Identities
    In this unit you will learn more about the trigonometric functions. In order to use them for solving real-world problems, you need to know more about their relationships with each other through the various trigonometric identities.
    6 More Trigonometric Identities; Applications involving triangles that are not right triangles
    This unit consists of two parts.
  • The first part finishes the study of trigonometric identities begun in Unit 5. In this section you will use the various trigonometric identities to help solve equations involving trigonometric functions.
  • The second part is a study of methods for solving general triangles, using the Law of Sines and the Law of Cosines. Included are many different applications, along with a short section on two new formulas for the area of a triangle.
    • Trig Final TRIGONOMETRY FINAL EXAM
    Material covered: All Material from Units 1 through 6.
    7 Polar Coordinates; Polar Equations; Complex Numbers
    The Analytic Geometry section of the course begins with this unit, which consists of two parts.
  • The first is an introduction to polar coordinates for points in the xy-plane, and polar equations and their graphs.
  • The second is a study of complex numbers. The two topics are related by the polar form of a complex number, which then leads to simple formulas for finding powers and roots of complex number via DeMoivre's Theorem.
    • 8 Conic Sections (Standard position)
    This unit begins our study of the conic sections: parabolas, ellipses, and hyperbolas. We will only consider conics in standard position (parabolas with vertex at the origin, ellipses and hyperbolas with center at the origin), and in standard orientation in this unit. We will study translated conics and rotated conics in Unit 9.
    9 Conic Sections (translated and/or rotated); parametric equations
    In this unit, we continue our study of the conic sections with investigations on translation and rotation of axes. The course concludes with a study of parametric equations.
    Final ANALYTIC GEOMETRY FINAL EXAM
    Material covered: All Material from Units 7, 8, 9.
    For details, see calendar, and click on the unit link for that unit's detailed description ~or~ click on the unit number above.

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