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Mathematics LibreTexts

1: Foundations of Trigonometry

  • Page ID
    69459
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    • 1.1: Angles and their Measure
      This section begins our study of Trigonometry and to get started, we recall some basic definitions from Geometry. A ray is usually described as a `half-line' and can be thought of as a line segment in which one of the two endpoints is pushed off infinitely distant from the other, as pictured below. The point from which the ray originates is called the initial point of the ray.
    • 1.2: The Unit Circle- Cosine and Sine
    • 1.3: The Six Circular Functions and Fundamental Identities
      We previously defined cos(θ) and sin(θ) for angles θ using the coordinate values of points on the Unit Circle. As such, these functions earn the moniker circular functions (we will start using the phrase `trigonometric function' interchangeably with the term `circular function'). It turns out that cosine and sine are just two of the six commonly used circular functions which we define in this Module.
    • 1.4: Trigonometric Identities
      Our first set of identities is the `Even / Odd' identities.The properties of the circular functions when thought of as functions of angles in radian measure hold equally well if we view these functions as functions of real numbers. Not surprisingly, the Even / Odd properties of the circular functions are so named because they identify cosine and secant as even functions, while the remaining four circular functions are odd.
    • 1.5: Graphs of the Trigonometric Functions
      In this section, we return to our discussion of the circular (trigonometric) functions as functions of real numbers.. As usual, we begin our study with the functions f(t)=cos(t) and g(t)=sin(t).
    • 1.6: The Inverse Trigonometric Functions
      In this section we concern ourselves with finding inverses of the (circular) trigonometric functions. Our immediate problem is that, owing to their periodic nature, none of the six circular functions is one-to-one. To remedy this, we restrict the domains of the circular functions in the same way we restricted the domain of the quadratic function previously.
    • 1.7: Trigonometric Equations and Inequalities
    • 1.E: Foundations of Trigonometry (Exercises)
      These are homework exercises to accompany Chapter 10 of Stitz and Zeager's "Pre-Calculus" Textmap.

    Contributors and Attributions

    • Carl Stitz, Ph.D. (Lakeland Community College) and Jeff Zeager, Ph.D. (Lorain County Community College)

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