20
votes
Accepted
Real-life problems involving solving triangles
There are many real-life problems involving solving triangles in "Trigonometry for the Practical Man" by James Edgar Thompson. Here are some from Chapter 5:
Problem 1
From the top of a ...
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16
votes
Accepted
Why is it written $\tan^{-1}$?
It's the functional inverse rather than the multiplicative inverse. Somewhere along the way, notation arrived at function composition being written as $f(f(x))=f^2(x)$, so the functional inverse ...
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10
votes
Why is it written $\tan^{-1}$?
I will start by noting that I have written an answer to a similar question on Mathematics SE, and would direct you towards that answer for some additional discussion.
In my precalculus class, I tend ...
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9
votes
What is this symbol called?
Please check the entire Greek alphabet, as you can find it in this Wikipedia page: https://en.wikipedia.org/wiki/Greek_alphabet.
I must add that there are two ways to write the letter $phi$ in MathJax ...
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9
votes
What is this symbol called?
That's lowercase Greek phi, pronounced with an initial f sound and rhyming with English pie, lie or sky. That said, some speakers may pronounce it rhyming with English see, key or me.
See https://en.m....
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8
votes
Real-life problems involving solving triangles
I’ve got one very specific answer to this question, because I had to dust off my old trigonometry knowledge just yesterday. I tell it as a real-world use of what I had to learn in school out of left ...
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5
votes
Symmetry in polar functions - how to explain
A given point with polar coordinates $(r, \theta)$ has a doubly infinite set of representations $(r,\theta+2n\pi)$ and $(-r,\theta+(2n+1)\pi)$, for integer $n$. When checking for symmetry they should ...
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4
votes
Real-life problems involving solving triangles
Triangulation (Wikipedia link) has a wide variety of real-world uses. As a wildlife ecologist, a particularly fun one I can think of is wildlife radio telemetry (Wikipedia link). In this case, a radio ...
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3
votes
Real-life problems involving solving triangles
One of the classic problems is have them calculate the height of a building. This can be your school building if you want.
Given a tall enough building, or an irregularly shaped building, pulling a ...
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3
votes
Why is it written $\tan^{-1}$?
Once we understand the reason $\tan^{-1}$ can mean the inverse tangent and that most people prefer to write this function as $\arctan$, your neighbor's daughter's question brings up an issue that ...
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3
votes
Symmetry in polar functions - how to explain
If we applied two tests for each symmetry (one with 𝑟
and one with −𝑟
), are there any equations that would still "get away" undetected?
This is a question that came up recently in my ...
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2
votes
Real-life problems involving solving triangles
A caveat: I work in computer vision, so my perspective my be a little biased by a desire to "evangelize" on a currently hot topic.
Students these days spend a lot of spare time looking at ...
2
votes
Interesting Trigonometry problems
I would like to suggest following challenges,
Geometric proof of sum and product of three tangents of a triangle are equal for obtuse-angled triangles.
(https://www.janakasrodrigo.com/wp-content/...
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2
votes
Real-life problems involving solving triangles
Squares and hexagons can be decomposed into triangles. This opens up a lot of practical problems that I encounter, such as:
What is the largest hexagon that can fit into a circle? (you just need the ...
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2
votes
What is this symbol called?
For such a query, you might find it quicker to use one of the following tools:
Google Image Reverse Search: Navigate to google.com and upload an image of the symbol. Google will display similar ...
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1
vote
Real-life problems involving solving triangles
Most college textbooks for trig have some good problems. (For example, see page 43 of this pdf: https://www.slcc.edu/math/docs/math-1060-oer-trigonometry-textbook-version-2.pdf)
(When you get to sine ...
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1
vote
How to teach relationship between slopes and angles?
Maybe start discussion with photos something like:
Sign indicating a 10% grade at the base of hill. What does it mean?
https://www.shutterstock.com/image-photo/road-sign-steep-slope-105861944
Picture ...
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1
vote
Symmetry in polar functions - how to explain
If a textbook gives symmetry tests for graphs of polar equations without stating that they are sufficient but not necessary, that's a glaring omission, in my opinion. I looked through several books, ...
- 3,160
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