The Comprehensive Guide to Understanding the Key Elements of Plane Trigonometry by Stephen Fisher: Learn Easily Without Getting Overwhelmed

An to Plane Trigonometry

Plane trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles in two-dimensional space, also known as a plane. It can be considered as an essential foundation for advanced mathematical concepts and various fields, including physics, engineering, astronomy, and navigation.

The Legacy of Stephen Fisher

Stephen Fisher, a celebrated mathematician and educator, played a crucial role in the development and popularization of plane trigonometry. His groundbreaking book, "Elements of Plane Trigonometry," revolutionized the way students learn and understand this complex subject. Fisher's approach simplifies complex concepts, making trigonometry accessible and enjoyable for learners of all levels.

The Basic Elements of Plane Trigonometry

1. Angles: In plane trigonometry, angles are measured in degrees or radians and form the basis for understanding trigonometric functions.

Elements of Plane Trigonometry

by Stephen D. Fisher (Kindle Edition)

4.2 out of 5

Language	:	English
File size	:	2083 KB
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2. Right Triangles: Right triangles are one of the fundamental building blocks of trigonometry. They consist of one angle measuring 90 degrees and two other angles varying from 0 to 89 degrees.

3. Trigonometric Functions: Trigonometric functions, such as sine, cosine, and tangent, are used to relate the angles of a triangle to the lengths of its sides.

4. Laws of Trigonometry: These laws, including the Pythagorean theorem, sine rule, and cosine rule, enable the calculation of unknown angles and side lengths within a triangle.

The Importance of Plane Trigonometry

Understanding plane trigonometry is highly beneficial in various real-world applications. Some of these include:

• Astronomy: Trigonometry helps calculate the distances between celestial bodies, determine their positions, and study their movements.
• Navigation: Trigonometry enables sailors and pilots to navigate accurately by calculating distances, angles, and trajectories.
• Architecture: Architects use trigonometry to measure angles, determine heights, create accurate blueprints, and ensure structural stability.
• Engineering: Trigonometry is vital in engineering fields, such as civil, mechanical, and electrical, for designing structures and solving complex design problems.
• Physics: Trigonometric principles are extensively used in physics, particularly when dealing with waves, vibrations, and oscillations.

Tips for Mastering Plane Trigonometry

1. Understand the Basics: Familiarize yourself with angles, right triangles, trigonometric functions, and the laws of trigonometry. These foundational concepts will serve as a solid base for further learning.

2. Practice Regularly: Solve a variety of trigonometry problems to reinforce your understanding and develop problem-solving skills.

3. Visualize: Utilize visual aids, such as diagrams and graphs, to visualize and comprehend trigonometric concepts.

4. Seek Guidance: If you encounter difficulties, don't hesitate to seek help from teachers, online resources, or study groups. Trigonometry can be challenging, but with the right support, success is within reach.

Plane trigonometry, as expounded by Stephen Fisher in his book "Elements of Plane Trigonometry," is a fascinating and indispensable field of mathematics. By understanding its key elements, such as angles, right triangles, trigonometric functions, and laws, you unlock a world of possibilities in various scientific and practical domains. With dedication, practice, and the right approach, you can master plane trigonometry and open doors to a host of exciting opportunities.

Elements of Plane Trigonometry

by Stephen D. Fisher (Kindle Edition)

4.2 out of 5

Language	:	English
File size	:	2083 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Print length	:	134 pages
Lending	:	Enabled
X-Ray for textbooks	:	Enabled

FREE

Elements of Plane Trigonometry by Hugh Blackburn, M.A.

Some apology is required for adding another to the long list of books on Trigonometry. My excuse is that during twenty years' experience I have not found any published book exactly suiting the wants of my Students. In conducting a Junior Class by regular progressive steps from Euclid and Elementary Algebra to Trigonometry, I have had to fill up by oral instruction the gap between the Sixth Book of Euclid and the circular measurement of Angles; which is not satisfactorily bridged by the propositions of Euclid's Tenth and Twelfth Books usually supposed to be learned; nor yet by demonstrations in the modern books on Trigonometry, seemed to me defective for modern requirements, as not sufficiently connected with Analytical Trigonometry.

What I felt the want of was a short Treatise, to be used as a Text Book after the Sixth Book of Euclid had been learned and some knowledge of Algebra acquired, which should contain satisfactory demonstrations of the propositions to be used in teaching Junior Students the Solution of Triangles, and should at the same time lay a solid foundation for the study of Analytical Trigonometry.

This want I have attempted to supply by applying, in the First Chapter, Newton's Method of Limits to the mensuration of circular arcs and areas; choosing that method both because it is the strictest and the easiest, and because I think the Mathematical Student should be early introduced to the method.

The succeeding Chapters are devoted to an exposition of the nature of the Trigonometrical ratios, and to the demonstration by geometrical constructions of the principal propositions required for the Solution of Triangles. To these I have added a general explanation of the applications of these propositions in Trigonometrical Surveying: and I have concluded with a proof of the formula for the sine and cosine of the sum of two angles treated (as it seems to me they should be) as examples of the Elementary Theory of Projection.

Having learned thus much the Student has gained knowledge of Trigonometry as originally understood, and may apply his knowledge in Surveying; and he has also reached a point from which he may advance into Analytical Trigonometry and its use in Natural Philosophy.

Thinking that others may have felt the same want as me, I have published the Tract instead of merely printing it for the use of my Class.

H. B.

Content

CHAPTER I - OF THE MENSURATION OF THE CIRCLE.

CHAPTER II - OF THE AREA OF A TRIANGLE AND OF THE INSCRIBED CIRCLE.

CHAPTER III - OF SYMBOLS OF QUANTITY

CHAPTER IV - OF THE UNIT OF ANGULAR MAGNITUDE

CHAPTER V - CIRCULAR FUNCTIONS, OR TRIGONOMETRICAL RATIOS.

CHAPTER VI - OF LOGARITHMIC TABLES.

CHAPTER VII - SOLUTION OF TRIANGLES.

CHAPTER VIII - OF TRIGONOMETRICAL SURVEYING

CHAPTER IX - OF PROJECTIONS.

CHAPTER X - THE SINE AND COSINE OF THE SUM AND DIFFERENCE OF TWO
ANGLES.