Math 1022 College Trigonometry

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

Applications of 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
NameLast Modified
Su24 Session B Math 1022 Syllabus for Section 1 [pdf]2024-05-20

Daily Schedule

Math 1022 College Daily Schedule
NameLast Modified
Su24 Session B Math 1022 Sec 1 Schedule [pdf]2024-05-20

Class Notes

Math 1022 College Trigonometry Class Notes
NameLast Modified
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 6.5 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 6.4 Right Triangle Trigonometry [docx]2023-05-21
Section 6.4 Right Triangle Trigonometry [pdf]2023-05-21
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

Videos

Section 6.1: Angles and Their Measure

Section 6.2: Applications of Radian Measure

Section 6.3: Triangles

Section 6.4: Right Triangle Trigonometry

Section 6.5: Trigonometric Functions of General Angles

Section 6.6: Unit Circle

Section 7.1: Graphs of Sine and Cosine Functions

Section 7.2: More on Graphs of Sine and Cosine Functions

Section 7.3: Graphing Tangent, Cotangent, Secant, and Cosecant Functions

Section 7.4: Inverse Trigonometric Functions I

Section 7.5: Inverse Trigonometric Functions II

Section 8.1: Trigonometric Identities

Section 8.2: Sum and Difference Formulas

Section 8.3: Double-Angle and Half-Angle Formulas

Section 8.5: Trigonometric Equations

Section 9.1: Applications Involving Right Triangles

Section 9.2: The Law of Sines

Section 9.3: The Law of Cosines

Section 9.4: Area of a Triangle

Section 10.1: Polar Coordinate System

Section 10.2: Graphing Polar Equations

Section 10.4: Vectors

Course Coordinator

Photo of Selena Oswalt

Selena Oswalt
Math 1022 Coordinator
Office: 206 Lockett Hall
Office hours: M 12:30pm–2:00pm; W 10:00am–11:00am
Telephone: +1 225 578 1563
Email: soswal2@lsu.edu