Dual Enrollment Program DE Course: Math 1022 Plane Trigonometry
Dual Enrollment Program DE Course: Math 1022 Plane Trigonometry
Math 1022 College Trigonometry provides an in-depth treatment of trigonometric functions with applications; trigonometric graphs with transformations; inverse trigonometric functions; fundamental identities and angle formulas; solving equations; triangles with applications; polar coordinate system.
This is an LSU Integrative Learning Core (ILC) course that awards general education credit.
Note: Math 1022 is taught in the spring semester usually following Math 1021 in the fall. It is designed for students who plan to major in a STEM field or in non-STEM fields which require it, such as kinesiology, construction management, psychology, agriculture, and others. It also is used to prepare students for success in calculus. Students will need only one MyLab Math access code for the Math 1021/1022 sequence.
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 & Pacing Guide
| Name | Last Modified |
|---|---|
| S26 Math 1022 DE Syllabus [docx] | 2025-12-10 |
| S26 Math 1022 DE Pacing Guide [docx] | 2025-12-10 |
Course Profile
| Name | Last Modified |
|---|---|
| Math 1022 Trigonometry COURSE PROFILE 6-12-2024 [docx] | 2024-06-13 |