# Math 1022 College Trigonometry

## Precalculus Program

Math 1022 College Trigonometry provides an in-depth treatment of functions and graphs; inverse trigonometric functions; fundamental identities and angle formulas; solving equations; triangles with applications; polar coordinate system.

## Course Eligibility

To enroll in Math 1022, you must have credit in Math 1021, obtainable as follows:

• Taking and passing Math 1021; or,
• Math ACT score of 25 or greater; or,
• ALEKS test of 61 or greater; or,
• Math SAT score of 590 or greater.

## Topics and Objectives

### An Introduction to Angles: Degree and Radian Measure

• Understanding degree measure and radian measure
• Converting between degree measure and radian measure
• Finding coterminal angles using degree measure and radian measure

• Determining the area of a sector of a circle
• Determining the arc length of a sector of a circle

### Triangles (Review)

• Classifying triangles
• Using the Pythagorean Theorem
• Understanding similar triangles
• Understanding the special right triangles

### Right Triangle Trigonometry

• Understanding the right triangle definitions of the trigonometric functions
• Using the special right triangles
• Understanding the fundamental trigonometric identities
• Understanding cofunctions
• Evaluating trigonometric functions using a calculator

### Trigonometric Functions of General Angles

• Understanding the four families of special angles
• Understanding the definitions of the trigonometric functions of general angles
• Finding the values of the trigonometric functions of quadrantal angles
• Understanding the signs of the trigonometric functions
• Determining reference angles
• Evaluating trigonometric functions of angles belonging to the $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$ families

### The Unit Circle

• Understanding the definition of the unit circle
• Understanding the unit circle definitions of the trigonometric functions

### The Graphs of the Trigonometric Functions

• Understanding the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions and their properties
• Sketching graphs of the form $y=A\sin(Bx-C)+D$ or $y=A\cos(Bx-C)+D$
• Sketching graphs of the form $y=A\tan(Bx-C)+D$ or $y=A\cot(Bx-C)+D$
• Sketching graphs of the form $y=A\sec(Bx-C)+D$ or $y=A\csc(Bx-C)+D$
• Determine the equation of a function of the form $y=A\sin(Bx-C)$ or $y=A\cos(Bx-C)$ given its graph

### Inverse Trigonometric Functions

• Understanding and finding the exact and approximate values of the inverse sine function, the inverse cosine function, and the inverse tangent function
• Evaluating composite functions involving inverse trigonometric functions of the forms $f∘f^{-1}$, $f^{-1}∘f$, $f∘g^{-1}$, and $f^{-1}∘g$

### Trigonometric Identities

• Substituting known identities to verify an identity
• Changing to sines and cosines to verify an identity
• Factoring to verify an identity
• Separating a single quotient into multiple quotients to verify an identity
• Combining fractional expressions to verify an identity
• Multiplying by conjugates to verify an identity

### The Sum and Difference Formulas

• Understanding and using the sum and difference formulas for the cosine, sine, and tangent functions
• Using the sum and difference formulas to verify identities
• Using the sum and difference formulas to evaluate expressions involving inverse trigonometric functions

### The Double-Angle and Half-Angle Formulas

• Understanding and using the double-angle formulas and the half-angle formulas
• Using the double-angle and half-angle formulas to verify identities
• Using the double-angle and half-angle formulas to evaluate expressions involving inverse trigonometric functions

### Trigonometric Equations

• Solving trigonometric equations that are linear or quadratic in form
• Solving trigonometric equations using identities
• Solving other types of trigonometric equations
• Solving trigonometric equations using a calculator

### Right Triangle Applications

• Solving right triangles
• Solving applications using right triangles

### The Law of Sines

• Determining if the Law of Sines can be used to solve an oblique triangle
• Using the Law of Sines to solve the SAA case or the ASA case
• Using the Law of Sines to solve the SSA (Ambiguous) case
• Using the Law of Sines to solve applied problems involving oblique triangles

### The Law of Cosines

• Determining if the Law of Cosines can be used to solve an oblique triangle
• Using the Law of Cosines to solve the SAS case
• Using the Law of Cosines to solve the SSS case
• Using the Law of Cosines to solve applied problems involving oblique triangles

### Area of Triangles

• Determining the area of oblique triangles
• Using Heron’s Formula to determine the area of an SSS triangle
• Solving applied problems involving the area of triangles

### Polar Coordinates and Polar Equations

• Plotting points using polar coordinates
• Determining different representations of a point (r, θ)
• Converting points from polar to rectangular coordinates and from rectangular to polar coordinates
• Converting equations from rectangular to polar form and from polar to rectangular form

### Graphing Polar Equations

• Sketching equations of the form $r\cosθ = a$, $r\sinθ = a$, $ar\cosθ + br\sinθ = c$, and $θ = α$
• Sketching equations of the form $r = a$, $r = a\sinθ$, and $r = a\cosθ$
• Sketching equations of the form $r = a + b\sinθ$ and $r = a + b\cosθ$
• Sketching equations of the form $r = a\sin(nθ)$ and $r = a\cos(nθ)$
• Sketching equations of the form $r^{2} = a^{2}\sin(2θ)$ and $r^{2} = a^{2}\cos(2θ)$

### Vectors

• Understanding the geometric representation of a vector
• Understanding operations on vectors represented geometrically
• Understanding vectors in terms of components
• Understanding vectors in terms of i and j
• Finding a unit vector
• Determining the direction angle of a vector
• Representing a vector in terms of i and j given its magnitude and direction angle
• Using vectors to solve applied problems involving velocity

## Syllabus

Math 1022 College Trigonometry Syllabus
F23 Math 1022 Syllabus for Sections 1-14 [pdf]2023-08-15
F23 Math 1022 Syllabus for Section 51 online [pdf]2023-08-15

## Daily Schedule

Math 1022 College Daily Schedule
F23 Math 1022 Schedule Monday [pdf]2023-08-15
F23 Math 1022 Schedule Wednesday [pdf]2023-08-15
F23 Math 1022 Schedule Friday [pdf]2023-08-15
F23 Math 1022 Schedule Online [pdf]2023-08-15

## Class Notes

Math 1022 College Trigonometry Class Notes
Section 6.1 An Introduction to Angles: Degree and Radian Measure [docx]2023-05-20
Section 6.1 An Introduction to Angles: Degree and Radian Measure [pdf]2023-05-20
Section 6.2 Applications of Radian Measure [docx]2023-05-20
Section 6.2 Applications of Radian Measure [pdf]2023-05-20
Section 6.3 Triangles [docx]2023-05-20
Section 6.3 Triangles [pdf]2023-05-20
Section 6.4 Right Triangle Trigonometry [docx]2023-05-21
Section 6.4 Right Triangle Trigonometry [pdf]2023-05-21
Section 6.5 Trigonometric Functions of General Angles [docx]2023-05-20
Section 6.5 Trigonometric Functions of General Angles [pdf]2023-05-21
Section 6.6 The Unit Circle [docx]2023-05-20
Section 6.6 The Unit Circle [pdf]2023-05-20
Section 7.1 The Graphs of Sine and Cosine [docx]2023-05-20
Section 7.1 The Graphs of Sine and Cosine [pdf]2023-05-20
Section 7.2a More on the Graphs of Sine and Cosine: Phase Shift [docx]2023-05-20
Section 7.2a More on the Graphs of Sine and Cosine: Phase Shift [pdf]2023-05-20
Section 7.2b More on the Graphs of Sine and Cosine: Vertical Shift [docx]2023-05-20
Section 7.2b More on the Graphs of Sine and Cosine: Vertical Shift [pdf]2023-05-20
Section 7.3 Graphs of Tangent, Cotangent, Secant, and Cosecant [docx]2023-05-20
Section 7.3 Graphs of Tangent, Cotangent, Secant, and Cosecant [pdf]2023-05-20
Section 7.4 Inverse Trigonometric Functions I [docx]2023-05-20
Section 7.4 Inverse Trigonometric Functions I [pdf]2023-05-20
Section 7.5 Inverse Trigonometric Functions II [docx]2023-05-20
Section 7.5 Inverse Trigonometric Functions II [pdf]2023-05-20
Section 8.1 Trigonometric Identities [docx]2023-05-20
Section 8.1 Trigonometric Identities [pdf]2023-05-20
Math 1022 Formula Sheet for Test 3 and the Final Exam [pdf]2023-05-20
Section 8.2 The Sum and Difference Formulas [docx]2023-05-20
Section 8.2 The Sum and Difference Formulas [pdf]2023-05-20
Section 8.3 The Double-Angle and Half-Angle Formulas [docx]2023-05-20
Section 8.3 The Double-Angle and Half-Angle Formulas [pdf]2023-05-20
Section 8.5 Trigonometric Equations [docx]2023-05-20
Section 8.5 Trigonometric Equations [pdf]2023-05-20
Section 9.1 Right Triangle Applications [docx]2023-05-20
Section 9.1 Right Triangle Applications [pdf]2023-05-20
Section 9.2 The Law of Sines [docx]2023-05-21
Section 9.2 The Law of Sines [pdf]2023-05-21
Section 9.3 The Law of Cosines [docx]2023-05-20
Section 9.3 The Law of Cosines [pdf]2023-05-20
Section 9.4 Area of Triangles [docx]2023-05-20
Section 9.4 Area of Triangles [pdf]2023-05-20
Section 10.1 Polar Coordinates and Polar Equations [docx]2023-05-20
Section 10.1 Polar Coordinates and Polar Equations [pdf]2023-05-20
Section 10.2 Graphing Polar Equations [docx]2023-05-20
Section 10.2 Graphing Polar Equations [pdf]2023-05-20
Section 10.4 Vectors [docx]2023-05-20
Section 10.4 Vectors [pdf]2023-05-20

## Course Coordinator Selena Oswalt
Math 1022 Coordinator
Office: 206 Lockett Hall
Office hours: M 12:30pm–1:30pm; Tu 10:30am–12:30pm (LSU Math Lab); W 10:00am–11:00am
Telephone: +1 225 578 1563
Email: soswal2@lsu.edu