# 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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### Pythagoras and Trigonometry sequencing

In teaching the high school curriculum Pythagoras is usually bundled with Trigonometry. They might be justified by way of proof of some sort. They are used to solve 2d and 3d geometry problems for ...
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### Multiple proofs for the same problem

One way of encouraging students to explore mathematics can be letting them to use different approaches to solve the same problem. If students can find alternatives from different areas of mathematics ...
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### Simple way to explain Sine theorem applications

what is the simplest way to explain how to determine whether the resolution of a triangle (finding all its sides and angles, given 3 of them) using the sine theorem gives one or two solutions and ...
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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 ...
781 views

### 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/...
553 views

### 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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### 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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### 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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### 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 ...
1 vote
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### How to formulate this type of arcsin problem?

Reading and commenting on What are some common ways students get confused about finding an inverse of a function? I was kindly set straight that the use of $\sin^{^{-1}}(x)$ to mean $\arcsin(x)$ has ...
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### "Amplitude" of Tan and Cot functions

The amplitude of a sinusoid is the distance from its axis to a high point or a low point. When we read this, it follows that Tan and Cot don't have an amplitude. Nor do SEC or CSC. Now, I'm in an ...
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Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
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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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### 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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### 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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### Should word problems be reasonable?

I've recently run across a series of problems that didn't reflect reality. For example - An algebra problem with two teens on bicycles. The resulting times showed the bike was moving at 120MPH. ...
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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 ...
408 views

### 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 ...
417 views

### 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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