"Comprehensive Trigonometry Notes: Understanding Angles, Triangles, and Applications"
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Module
Trignometry
Institution
Trigonometry Notes: These concise notes provide an overview of trigonometry, a branch of mathematics that deals with the relationships between angles and sides of triangles. The notes cover fundamental concepts such as trigonometric functions (sine, cosine, tangent), angle measurement, special tria...
,Contents
Trigonometry – An Overview of Important Topics ....................................................................................... 4
UNDERSTAND HOW ANGLES ARE MEASURED ............................................................................................. 6
Degrees ..................................................................................................................................................... 7
Radians ...................................................................................................................................................... 7
Unit Circle.................................................................................................................................................. 9
Practice Problems ............................................................................................................................... 10
Solutions.............................................................................................................................................. 11
TRIGONOMETRIC FUNCTIONS .................................................................................................................... 12
Definitions of trig ratios and functions ................................................................................................... 12
Khan Academy video 2 ........................................................................................................................ 14
Find the value of trig functions given an angle measure ........................................................................ 15
Find a missing side length given an angle measure ................................................................................ 19
Khan Academy video 3 ........................................................................................................................ 19
Find an angle measure using trig functions ............................................................................................ 20
Practice Problems ............................................................................................................................... 21
Solutions.............................................................................................................................................. 24
USING DEFINITIONS AND FUNDAMENTAL IDENTITIES OF TRIG FUNCTIONS ............................................. 26
Fundamental Identities ........................................................................................................................... 26
Khan Academy video 4 ........................................................................................................................ 28
Sum and Difference Formulas................................................................................................................. 29
Khan Academy video 5 ........................................................................................................................ 31
Double and Half Angle Formulas ............................................................................................................ 32
Khan Academy video 6 ........................................................................................................................ 34
Product to Sum Formulas ....................................................................................................................... 35
Sum to Product Formulas ....................................................................................................................... 36
Law of Sines and Cosines ........................................................................................................................ 37
Practice Problems ............................................................................................................................... 39
Solutions.............................................................................................................................................. 42
UNDERSTAND KEY FEATURES OF GRAPHS OF TRIG FUNCTIONS ................................................................ 43
Graph of the sine function (𝒚 = 𝒔𝒊𝒏 𝒙) ................................................................................................ 44
Graph of the cosine function (𝒚 = 𝒄𝒐𝒔 𝒙) ............................................................................................ 45
2
, Key features of the sine and cosine function.......................................................................................... 46
Khan Academy video 7 ........................................................................................................................ 51
Graph of the tangent function (𝒚 = 𝒕𝒂𝒏 𝒙) ......................................................................................... 52
Key features of the tangent function ...................................................................................................... 53
Khan Academy video 8 ........................................................................................................................ 56
Graphing Trigonometric Functions using Technology ............................................................................ 57
Practice Problems ............................................................................................................................... 60
Solutions.............................................................................................................................................. 62
Rev. 05.06.2016-4
3
, Trigonometry – An Overview of Important Topics
So I hear you’re going to take a Calculus course? Good idea to brush up on your
Trigonometry!!
Trigonometry is a branch of mathematics that focuses on relationships between
the sides and angles of triangles. The word trigonometry comes from the Latin
derivative of Greek words for triangle (trigonon) and measure (metron).
Trigonometry (Trig) is an intricate piece of other branches of mathematics such
as, Geometry, Algebra, and Calculus.
In this tutorial we will go over the following topics.
Understand how angles are measured
o Degrees
o Radians
o Unit circle
o Practice
Solutions
Use trig functions to find information about right triangles
o Definition of trig ratios and functions
o Find the value of trig functions given an angle measure
o Find a missing side length given an angle measure
o Find an angle measure using trig functions
o Practice
Solutions
Use definitions and fundamental Identities of trig functions
o Fundamental Identities
o Sum and Difference Formulas
o Double and Half Angle Formulas
o Product to Sum Formulas
o Sum to Product Formulas
o Law of Sines and Cosines
o Practice
Solutions
4
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