Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

6: Additional Topics

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    • 6.1: Solving Trigonometric Equations
      In Chapter 1 we were concerned only with finding a single solution (say, between \(0^◦\text{  and }90^◦\) ). In this section we will be concerned with finding the most general solution to such trigonometric equations.
    • 6.2: Numerical Methods in Trigonometry
      We were able to solve the trigonometric equations in the previous section fairly easily, which in general is not the case. Instead, we have to resort to numerical methods, which provide ways of getting successively better approximations to the actual solution(s) to within any desired degree of accuracy.
    • 6.3: Complex Numbers
      There is no real number \(x\) such that \(x^ 2 = −1\). However, it turns out to be useful to invent such a number, called the imaginary unit and denoted by the letter i.
    • 6.4: Polar Coordinates
      Suppose that from the point (1,0) in the xy-coordinate plane we draw a spiral around the origin, such that the distance between any two points separated by \(360^\circ\) along the spiral is always 1, as in Figure 6.4.1. We can not express this spiral as \(y = f (x)\) for some function \(f\) in Cartesian coordinates, since its graph violates the vertical rule. However, this spiral would be simple to describe using the polar coordinate system.
    • 6.E: Additional Topics (Exercises)
      These are homework exercises to accompany Corral's "Elementary Trigonometry" Textmap. This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed.

    Thumbnail: This spiral would be complicated to quantify in Cartesian system, but is quite simple to describe using the polar coordinate system.

    6: Additional Topics is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Michael Corral via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.