# Chapter 1 Trigonometry

## Ch 1.1  Angles

Angle Basics – Ray, Positive Angle, Negative Angle, Degree, Acute, Obtuse, Right, Straight, and Reflex    angle, Complementary Angle, Supplementary Angle

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Animation: Types of Angles – Acute, Obtuse, Right, Straight, and Reflex angle

Adjacent, Complementary, Supplementary, and Vertical Angles

Degrees, Minutes, and Seconds

Animation: Angles in Standard Position

Finding the Quadrant in Which an Angle Lies :

Examples :45º, 195º, -20º, –72º, 340º, 120º

Examples :380º, 1240º, –445º

Examples :25º, –255º, –580º

Angles in Standard Position Quadrantal Angle, and Coterminal Angles :

Coterminal Angles of 135º, 1070º, –65º, 90º

Coterminal Angles of 45º, 135º, –255º, 90º

Determining if the pairs of angles are Coterminal Angles

Determining Positive and Negative Coterminal Angle of 68º

## Ch 1.2   Angle Relationships and Similar Triangles

Angle Relationships and Types of Triangles – Vertical Angle, Interior Angles, Equilateral Triangle, Isosceles Triangle, Scalene Triangle, Right Triangle, Acute Triangle, Obtuse Triangle, Sum of

Measures of Angles

Similar Polygons – Properties of Similar Polygons, Solve the Similar Triangles

Congruent and Similar Triangles – Conditions for Similar Triangles, Solve for Similar Triangles

Sum of Interior Angles in a Triangle

## Ch 1.3  Trigonometric Functions

Introduction to Six Trigonometric Functions Using Triangles – Sine, Cosine, Tangent, Secant, Cosecant, Cotangent

Introduction to Six Trigonometric Functions Using Angles (in a Unit Circle) – Sine, Cosine, Tangent, Secant, Cosecant, Cotangent

Six Trigonometric Functions of Quadrantal Angles (0º, 90º, 180º, 270º)

Finding The Trigonometric Function value based on a Coordinate :

Finding the Trigonometric Function values of Cotangent and Tangent with Coordinate of (3, 4)

Finding the Trigonometric Function value of Secant with Coordinate of (5, 6)

Finding the Trigonometric Function values of Sine and Cosine with coordinate of (7, –2)

Finding the Six Trigonometric Function Values with Coordinate of (10, –6)

## Ch 1.4  Using the Definitions of the Trigonometric Functions

Finding Trigonometric Function Values Given One Trig Value cos θ=5/12  in a Right Triangle

Finding the Area of the Triangle

Finding the Missing Length and Cotangent Value

Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities, and use identities to solve for angles :

Determining sec θ Given cos θ=2/3
Determining cot θ Given tan θ=5
Determining cos θ Given sec θ=-5/2
Finding sin θ and tan θ Given that cos θ=√3 /5 and sin θ>0
Finding sin θ and cos θ Given that tan θ= 5/12 and θ is in Quadrant III

Finding sin θ and tan θ Given that cos θ=3/4 and θ is in Quadrant IV
Finding sec θ and sin θ Given that cos θ=-5/3 and θ is in Quadrant II
Finding Six Exact Trigonometric Function Values Given the Point (–2, –4) on the Terminal Side of θ

Determining the Quadrant of the Terminal Side of an Angle Given Trig Function Signs