# Questions tagged [trigonometry]

For questions about effectively motivating and teaching the concepts of trigonometry, including the unit circle, the sin/cos/tan functions, and other related ideas.

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### Phase shift vs. horizontal shift, and frequency vs. angular frequency in sinusoidal functions

TL;DR version: It seems to me that high school curricula no longer distinguish between "horizontal shift" and "phase shift", or between "frequency" and "angular ...
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### The best way to introduce trigonometric functions in a rigorous analysis course

This is something I have always had issues with. Generally, three approaches are used: The geometric path: this follows the standard way how you would introduce these functions in school. The problem ...
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### How to intuitively understand how the trig ratios are calculated

I've asked a question on Math Stack Exchange, but it was suggested it might be a better idea to post it on this Educators instead. Here's the question link: https://math.stackexchange.com/questions/...
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### Python programming - math library that uses degrees by default [closed]

Other than the standard math module for Python3, is there another library out there that uses degrees by default (as opposed to radians)? I am teaching students to use turtle (which uses degrees by ...
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### Is Plane Trigonometry by S. L. Loney still good as a textbook today?

I am considering using S. L. Loney's Plane Trigonometry as the textbook for my course in trigonometry and would like to ask for opinions about the book. This books is very odd and there might be pros ...
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### The origins of $\operatorname{cis}(\theta)$

There is a abbreviation used in high school mathematics that is almost never seen outside of it: $\operatorname{cis}(\theta) = \cos(\theta) + i \sin(\theta)$, where cis stands for cosine + i sine. As ...
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### Memorizing Trig Identities

I adjunct for a local community college teaching College Algebra and College Trigonometry. Every year, the community college math department insists on students memorizing each of the trig identities....
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### Solving a Polar set of equations algebraically?

I was coaching a student on how to approach this problem. 2 equations given and the question was where they intersect. Now, with a bit of practice on polar coordinates, producing the graph by hand ...
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### Best Way to Learn Trigonometry

What are the best resources to learn trigometry? I recently decided to pursue a BS in mathematics at uni. I used to fail all my math classes with D's or F's until I started teaching myself, and so far ...
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### Pedagogical considerations behind current order of presentation of trigonometry

A pre-calculus book (Precalculus ed 1 By Miller and Gerken), presents trigonometry in the following order: 1- Angles 2- Trigonometric functions defined on the unit circle 3- Right triangle ...
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### Which textbooks on College Algebra, Trigonometry, Pre-calculus, Calculus, Linear Algebra, ODE are written by world-class mathematicians?

For example, Trigonometry was written by Wolf-Prize winner Israel Gelfand, one of the top mathematicians in the 20th century. I am wondering if other world-class mathematicians have written textbooks ...
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### Symmetry in polar functions - how to explain

In the precalculus curriculum I am teaching (using Stewart's book Precalculus: Mathematics for Calculus, 7th ed.), we do a bit of polar graphing, which includes discussion of symmetry on polar graphs. ...
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### How important is knowledge of trig identities for use in Calculus

I have a question regarding tutoring a calculus student. They need to prove trig identities such as $$\frac{1}{1-\sin x}+\frac{1}{1+\sin x}=2\sec^2x.$$ Doing this kind of problem is very tedious and ...
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### Resources on 3D transforms, vectors, coordinate systems

Background: I'm helping engineers use software to create 3D geometry in a programmatic way (similar to OpenSCAD). The functions they need to call have inputs which are low-level geometry concepts: 3D ...
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### Rules to eliminate erroneous solutions in Trig equations?

This is a High School Trig problem asking for the solution to an otherwise simple equation. $\frac{\left(1+\cos x\right)}{\sin x}$=-1 (per comment - the domain was specified as greater than -180 ...
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### Unit circle vs. ratios of right triangles vs. wave functions for introducing trig functions

In an introductory trignometry course, there are many options for introducing trigonometric functions: As ratios of sides of right triangles As coordinates (or ratios of coordinates) of intersections ...
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### Necessary trigonometric identities for k-12 students [closed]

Which trigonometric identities are necessary for the k-12 student? I want to make a list of trigonometruc identities for k-12 student. My list is below, please help me to improve the list by ...
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### Pi or Tau? How should the circle constant be taught?

Tau ($\tau = 2 \pi$) has more merits in its application, but pi is the established standard in industry and education. Is the trade-off of teach-ability of circle concepts worth the subsequent ...
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### Rigorously defining the concept of an angle for high school students

Arriving at a rigorous definition of the concept of angle for high school students is not as easy as expected. Google search provided me with many definition that are too technical or too vague IMO. ...
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### Trigonometric angles of rotation

I find that the notion of trigonometric angles of rotation is a bit confusing for the students. In my curriculum, students learn about angles first time at geometry in middle-school. The angles are "...
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### Why do we conventionally treat trig functions as going anti-clockwise from the right?

I realise that teachers tend to focus on right-angled triangles when introducing trig functions, and for those I can see that the most intuitive approach seems to be starting with the opposite and ...
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### Why are degree angle-measurements taught?

Apologies if this question has some obvious answer. Why are degrees still taught as a measure for angles, to be replaced later by radians (probably confusing many people), rather than just starting ...
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### Examples of Mathematical Beauty in School Mathematics

Various branches of mathematics have mathematical beauty. Some of this are visual, such as the mandelbrot set, while others are logically sublime, such as the recursive simplicities of peano ...
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### What purpose do these kinds of question serve in mathematical training?

The question in the picture is a relatively easy one to answer. But while learning Trigonometry, I had to answer countless questions asking to prove certain relations between obscure and complicated ...
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### How to convince the students of grade 8 that $\sin 90^\circ =1$? ( calculator not allowed )

In general the secondary student may not ask why is $\sin 90^\circ = 1$ because they can see the answer in the graph of the sine wave. However the students in grade 8 are not familiar with the graph ...
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### Examples of when $\tan(x) = \frac{\sin(x)}{\cos(x)}$ is useful

I'm making a video right now about the unit circle definitions of the basic trig functions. I've done sine and cosine, and am now talking about the tangent function. As most of you know, it can be ...
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### Proving trigonometric identities

When teaching trigonometric identities, I found the students had trouble proving them. All the students taking turns to ask almost all the questions of an exercise embarrased me somewhat. In order to ...