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Summary Basics of trignometry
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Trigonometry: Basics and ApplicationsPythagoras Theorem Applications
Application of the Pythagorean theorem to find
unknown sides of a right-angled triangle
Derivation of the formula $a^2 + b^2 = c^2$
Right Triangles and Trigonometric Functions
Definition of trigonometric functions in terms of
ratios of sides of a right-angled triangle
The relationship between the angles and the ratios
of the sides
Using right triangles to solve for unknowns using
trigonometry
Trigonometric Ratios Introduction
Introduction to sine, cosine, and tangent
How to calculate trigonometric ratios for given
angles
Trigonometric Ratio Relations
The relationships between the different
trigonometric ratios (sine, cosine, tangent)
Using these relationships to find the value of one
trigonometric ratio given the value of another
Angle Identities in Trigonometry
Trigonometric identities for complementary and
supplementary angles
Using these identities to simplify trigonometric
expressions and solve equations
, Importance of the Right Angle Triangle
Explanation of why right triangles are important in
trigonometry
How right triangles are used to solve real-world
problems using trigonometry
Triangle Identification and Solutions
Identifying different types of triangles (right,
isosceles, equilateral)
Using trigonometry to find unknown sides and
angles in triangles
Trigonometric Tables
Explanation of trigonometric tables and how they
were historically used
Comparison to calculator and computer-based
methods for calculating trigonometric values
Square Relations in Trigonometry
Discuss the Pythagorean identity $\sin^2(x) + \
cos^2(x) = 1$
The relationship between the square of sine and
cosine for any angle $x$
There are more related topics in trigonometry which are
not mentioned above, such as inverse trigonometric
functions, trigonometric equations, etc. These notes focus
on the basic concepts and applications of trigonometry in
right triangles.
Importance of the Right Angle Triangle
Right angle triangles are important in various
mathematical and real-life applications, including:
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