# 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

Name | Last Modified |
---|---|

Su23 Session B May 22 - June 24 Math 1022 Syllabus for Section 1 [pdf] | 2023-05-20 |

Su23 Session C July 3 - August 5 Math 1022 Syllabus for Section 2 [pdf] | 2023-05-20 |

## Daily Schedule

Name | Last Modified |
---|---|

Su23 Session B May 22 - June 24 Math 1022 Sec 1 Daily Schedule [pdf] | 2023-05-20 |

Su23 Session C July 3 - August 5 Math 1022 Sec 2 Schedule [docx] | 2023-05-20 |

## Class Notes

## 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: Polar Graphs

### Section 10.4: Vectors

## Course Coordinator

Selena Oswalt

Math 1022 Coordinator

Office: 206 Lockett Hall

Telephone: +1 225 578 1563

Email: soswal2@lsu.edu