Chapter 1: Angles and Trigonometric Functions
- Page ID
- 113905
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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
- One of the goals of this section is describe the position of such an object. To that end, consider an angle θ in standard position and let P denote the point where the terminal side of θ intersects the Unit Circle. By associating the point P with the angle θ , we are assigning a position on the Unit Circle to the angle θ .
- 1.3: 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.
- 1.4: 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.