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2: Periodic Functions and Non-Right Triangles

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    In this chapter, we will investigate graphs of sine, cosine, and other trigonometric functions.

    • 2.1: Prelude to Periodic Functions
      Each day, the sun rises in an easterly direction, approaches some maximum height relative to the celestial equator, and sets in a westerly direction. The pattern of the sun’s motion throughout the course of a year is a periodic function. Creating a visual representation of a periodic function in the form of a graph can help us analyze the properties of the function.
    • 2.2: Graphs of the Sine and Cosine Functions
      In the chapter on Trigonometric Functions, we examined trigonometric functions such as the sine function. In this section, we will interpret and create graphs of sine and cosine functions
    • 2.3: Graphs of the Other Trigonometric Functions
      This section addresses the graphing of the Tangent, Cosecant, Secant, and Cotangent curves.
    • 2.4: Inverse Trigonometric Functions
      In this section, we will explore the inverse trigonometric functions. Inverse trigonometric functions “undoes” what the original trigonometric function “does,” as is the case with any other function and its inverse. In other words, the domain of the inverse function is the range of the original function, and vice versa.
    • 2.5: Non-right Triangles - Law of Sines
      In this section, we will find out how to solve problems involving non-right triangles. The Law of Sines can be used to solve oblique triangles. According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side. There are three possible cases: ASA, AAS, SSA. Depending on the information given, we can choose the appropriate equation to find the requested solution.
    • 2.6: Non-right Triangles - Law of Cosines
      Unfortunately, while the Law of Sines enables us to address many non-right triangle cases, it does not help us with triangles where the known angle is between two known sides, a SAS (side-angle-side) triangle, or when all three sides are known, but no angles are known, a SSS (side-side-side) triangle. In this section, we will investigate another tool for solving oblique triangles described by these last two cases.
    • 2.7: Modeling with Trigonometric Equations
      Many natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model an equation to reflect periodic behavior? First, we must collect and record data. We then find a function that resembles an observed pattern and alter the function to get adependable model. Here. we will take a deeper look at specific types of periodic behavior and model equations to fit data.
    • 2.E: Periodic Functions (Exercises)
    • 2.R: Periodic Functions (Review)

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