# Perfect material for trigonometry

• archaic
In summary: Still very tough. With time and thinking, I am able to understand the red triangle and the lower blue triangle for the figure on the left. I have not understood beyond those yet.I am starting to see how the figure on the left can instead of being displayed all at one time, could be drawn IN STEPS, and then label the parts during each step. From these, begin examining the triangles in this sequence:red middle blue lower rightblue upper rightpink leftNow knowing these all compose the rectangle, the sine of sum of the two angles can be concluded.
archaic
The illustrations on this website are perfect.
http://trigonography.com/toc/

I hope it'll help!

Merlin3189, vanhees71, rsk and 4 others
Good stuff!

archaic
Doc Al said:
Good stuff!
Plus one on that.

I don't remember seeing figures like this (maybe I was sleeping in trig class that day). The angle-sum formulas and such were always a memory/lookup thing for me. Next time I can draw a little sketch and figure them out.

These figures, the two diagrams, are complicated for me. Maybe I have lost something in the last several years.

Some of the books I used showed derivations from graphs, which although complicated, after examining them carefully for a long time, I was able to understand. Learning to recreate some of the graphs might be a way for some people to figure how to get some of the formulas.

There is a good graph and derivation shown for Law Of Cosines, in of all places, the big thick Calculus book by Anton; a book I never used for any course but found the copy at a used-book sale.

archaic
symbolipoint said:
These figures, the two diagrams, are complicated for me. Maybe I have lost something in the last several years.

Some of the books I used showed derivations from graphs, which although complicated, after examining them carefully for a long time, I was able to understand. Learning to recreate some of the graphs might be a way for some people to figure how to get some of the formulas.

There is a good graph and derivation shown for Law Of Cosines, in of all places, the big thick Calculus book by Anton; a book I never used for any course but found the copy at a used-book sale.
Look at the left graph, the side which is equal to ##\sin{(\alpha+\beta)}## is equal to the opposite side since this is a rectange, you reason the same way for the rest, for the cosine you'll be substracting what's left of the side from the opposite one.

archaic said:
Look at the left graph, the side which is equal to ##\sin{(\alpha+\beta)}## is equal to the opposite side since this is a rectange, you reason the same way for the rest, for the cosine you'll be substracting what's left of the side from the opposite one.
Still very tough. With time and thinking, I am able to understand the red triangle and the lower blue triangle for the figure on the left. I have not understood beyond those yet.

I am starting to see how the figure on the left can instead of being displayed all at one time, could be drawn IN STEPS, and then label the parts during each step. From these, begin examining the triangles in this sequence:
1. red middle
2. blue lower right
3. blue upper right
4. pink left

Now knowing these all compose the rectangle, the sine of sum of the two angles can be concluded.

## 1. What is the definition of a perfect material for trigonometry?

A perfect material for trigonometry is a material that has the properties and characteristics necessary for accurately studying and solving trigonometric equations and problems. This includes being able to measure angles and distances with precision and having a consistent and reliable surface for drawing and graphing.

## 2. What are the qualities that make a material suitable for studying trigonometry?

The ideal material for studying trigonometry should be lightweight, easy to manipulate, and have a smooth and flat surface. It should also have markings or gridlines that aid in accurately measuring angles and distances. Additionally, the material should have minimal distortion and be able to withstand wear and tear from constant use.

## 3. Can any material be used for studying trigonometry?

While any material can technically be used for studying trigonometry, some materials are more suitable than others. For example, paper or cardboard may be too flimsy and easily damaged, while metal or plastic may be too heavy and difficult to manipulate. It is best to use a material specifically designed for trigonometry, such as a protractor or trigonometric table.

## 4. Is there a specific shape or size that is best for a material used in trigonometry?

The most commonly used material for trigonometry is a protractor, which is typically circular in shape with a diameter of 6 inches or more. However, other shapes and sizes, such as a triangle or a ruler, can also be effective for certain types of trigonometric problems. Ultimately, the best shape and size will depend on the specific needs of the user.

## 5. Are there any materials that should be avoided for studying trigonometry?

Materials that are not flat, such as a crumpled piece of paper or a curved surface, should be avoided for studying trigonometry as they can affect the accuracy of measurements and calculations. Materials that are easily distorted, such as fabric or rubber, should also be avoided. It is important to choose a material that is sturdy and will not easily bend or warp during use.

Replies
3
Views
2K
Replies
6
Views
2K
Replies
10
Views
3K
Replies
2
Views
2K
Replies
7
Views
1K
Replies
19
Views
2K
Replies
4
Views
1K
Replies
3
Views
3K
Replies
1
Views
1K
Replies
27
Views
4K