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2: Introduction to Trigonometry

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    The trigonometric functions are functions of an angle. and relate the angles of a triangle to the lengths of its sides. They are important in the study of triangles and modeling periodic phenomena, among many other applications.

    • 2.0: Prelude to Trigonometric Functions
      A function that repeats its values in regular intervals is known as a periodic function. The graphs of such functions show a general shape reflective of a pattern that keeps repeating. This means the graph of the function has the same output at exactly the same place in every cycle. And this translates to all the cycles of the function having exactly the same length.
    • 2.1: Angles - Radians and Degrees
      An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle. An angle is in standard position if its vertex is at the origin and its initial side lies along the positive x-axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.
    • 2.2: Unit Circle - Sine and Cosine Functions
      In this section, we will examine this type of revolving motion around a circle. To do so, we need to define the type of circle first, and then place that circle on a coordinate system. Then we can discuss circular motion in terms of the coordinate pairs.
    • 2.3: Right Triangle Trigonometry
      We have previously defined the sine and cosine of an angle in terms of the coordinates of a point on the unit circle intersected by the terminal side of the angle. In this section, we will see another way to define trigonometric functions using properties of right triangles.
    • 2.4: The Other Trigonometric Functions
      Trigonometric functions allow us to specify the shapes and proportions of objects independent of exact dimensions. We have already defined the sine and cosine functions of an angle. Though sine and cosine are the trigonometric functions most often used, there are four others. Together they make up the set of six trigonometric functions. In this section, we will investigate the remaining functions.
    • 2.5: Arcs, Angles, and Trig Function Values
      An angle is formed by rotating a ray about its endpoint. The ray in its initial position is called the initial side of the angle, and the position of the ray after it has been rotated is called the terminal side of the ray. The endpoint of the ray is called the vertex of the angle. When the terminal ray travels through all four quadrants the coordinate point along the unit circle will change value according to a special pattern.
    • 2.E: Trigonometric Functions (Exercises)
    • 2.R: Trigonometric Functions (Review)
      We have previously defined the sine and cosine of an angle in terms of the coordinates of a point on the unit circle intersected by the terminal side of the angle. In this section, we will see another way to define trigonometric functions using properties of right triangles.

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    This page titled 2: Introduction to Trigonometry is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.