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
Chapter and section numbers refer to Algebra & Trigonometry, 4th edition
6.1 An Introduction to Angles: Degree and Radian Measure
(48 exercises)
- Understand degree measure
- Understand radian measure
- Convert between degree measure and radian measure
- Find coterminal angles using degree measure
- Find coterminal angles using radian measure
6.2 Applications of Radian Measure
(18 exercises)
- Determine the area of a sector of a circle
- Determine the arc length of a sector of a circle
6.3 Triangles
(18 exercises)
- Classify triangles
- Use the Pythagorean Theorem
- Understand similar triangles
- Understand the special right triangles
6.4 Right Triangle Trigonometry
(44 exercises)
- Understand the right triangle definitions of the trigonometric functions
- Use the special right triangles
- Understand the fundamental trigonometric identities
- Understand cofunctions
- Evaluate trigonometric functions using a calculator
6.5 Trigonometric Functions of General Angles
(73 exercises)
- Understand the four families of special angles
- Understand the definitions of the trigonometric functions of general angles
- Find the values of the trigonometric functions of quadrantal angles
- Understand the signs of the trigonometric functions
- Determine reference angles
- Evaluate trigonometric functions of angles belonging to the $\pi \over 3$, $\pi \over 4$, and $\pi \over 6$ families
6.6 The Unit Circle
(12 exercises)
- Understand the definition of the unit circle
- Understand the unit circle definitions of the trigonometric functions
7.1 Graphs of Sine and Cosine Functions
(45 exercises)
- Understand the graph of the sine function and its properties
- Understand the graph of the cosine function and its properties
- Determine properties and sketch graphs of the form $y = A \sin x$ and $y = A \cos x$
- Determine properties and sketch graphs of the form $y = \sin Bx$ and $y = \cos Bx$
- Determine properties and sketch graphs of the form $y = A \sin Bx$ and $y = A \cos Bx$
- Determine the equation of a function of the form $y = A \sin Bx$ and $y = A \cos Bx$ given its graph
7.2a More on the Graphs of Sine and Cosine: Phase Shift
(21 exercises)
- Determine properties and sketch graphs of the form $y = \sin(x-C)$ and $y = \cos(x-C)$
- Determine properties and sketch graphs of the form $y = A \sin(Bx-C)$ and $y = A \cos(Bx-C)$
7.2b More on the Graphs of Sine and Cosine: Vertical Shift
(15 exercises)
- Determine properties and sketch graphs of the form $y = A \sin(Bx-C) + D$ and $y = A \cos(Bx-C) + D$
7.3 The Graphs of Tangent, Cotangent, Cosecant, and Secant Functions
(34 exercises)
- Understand the graph of the tangent function and its properties
- Determine properties and sketch graphs of the form $y = A \tan(Bx-C) + D$
- Understand the graph of the cotangent function and its properties
- Determine properties and sketch graphs of the form $y = A \cot(Bx-C) + D$
- Understand the graphs of the cosecant and secant functions and their properties
7.4 Inverse Trigonometric Functions I
(35 exercises)
- Understand and find the exact and approximate values of the inverse sine function
- Understand and find the exact and approximate values of the inverse cosine function
- Understand and find the exact and approximate values of the inverse tangent function
7.5 Inverse Trigonometric Functions II
(38 exercises)
- Evaluate composite inverse trigonometric functions of the form $f\bigl( f^{-1}(x) \bigr)$ and $f^{-1}\bigl( f(x) \bigr)$
- Evaluate composite inverse trigonometric functions of the form $f\bigl( g^{-1}(x) \bigr)$ and $f^{-1}\bigl( g(x) \bigr)$
8.1 Trigonometric Identities
(33 exercises)
- Review and use the fundamental identities
- Verify trigonometric identities
8.2 The Sum and Difference Formulas
(35 exercises)
- Use the sum and difference formulas for the cosine function
- Use the sum and difference formulas for the sine function
- Use the sum and difference formulas for the tangent function
- Use sum and difference formulas to evaluate expressions involving inverse trig functions
8.3 The Double-Angle and Half-Angle Formulas
(46 exercises)
- Use the double-angle formulas
- Use the half-angle formulas
- Use the double-angle and half-angle formulas to evaluate expressions involving inverse trig functions
8.5 Trigonometric Equations
(43 exercises)
- Solve trigonometric equations that are linear in form
- Solve trigonometric equations that are quadratic in form
- Solve trigonometric equations using identities
- Solve trigonometric equations using a calculator
9.1 Right Triangle Applications
(16 exercises)
- Solve right triangles
- Solve applied problems using right triangles
9.2 The Law of Sines
(29 exercises)
- Determine if the Law of Sines can be used to solve an oblique triangle
- Use the Law of Sines to solve the SAA case or the ASA case
- Use the Law of Sines to solve the SSA (ambiguous) case
- Use the Law of Sines to solve applied problems involving oblique triangles
9.3 The Law of Cosines
(22 exercises)
- Determine whether Law of Sines or Cosines should be used to solve an oblique triangle
- Use the Law of Cosines to solve the SAS case
- Use the Law of Cosines to solve the SSS case
- Use the Law of Cosines to solve applied problems involving oblique triangles
9.4 Area of Triangles
(19 exercises)
- Determine the area of oblique triangles
- Use Heron’s Formula to determine the area of an SSS triangle
- Solve applied problems involving the area of triangles
10.1 Polar Coordinates and Equations
(62 exercises)
- Plotg points using polar coordinates
- Determine different representations of a point $(r, θ)$
- Convert from polar to rectangular coordinates
- Convert from rectangular to polar coordinates
- Convert equations from rectangular to polar form
- Convert equations from polar to rectangular form
10.2 Graphs of Polar Equations
(67 exercises)
- Sketch equations of the form $r \cos θ = a$, $r \sin θ = a$, $a r \cos θ + b r \sin θ = c$, and $θ = α$
- Sketch equations of the form $r = a$, $r = a \sin θ$, and $r = a \cos θ$
- Sketch equations of the form $r = a + b \sin θ$ and $r = a + b \cos θ$
- Sketch equations of the form $r = a \sin(nθ)$ and $r = a \cos(nθ)$
- Sketch equations of the form $r^2 = a^2 \sin(2θ)$ and $r^2 = a^2 \cos(2θ)$
10.4 Vectors
(31 exercises)
- Determine magnitudes of vectors that are represented geometrically
- Perform operations on vectors that are represented geometrically
- Determine components and magnitudes of vectors
- Write vectors in terms of $i$ and $j$
- Perform operations on vectors written in $a i + b j$ form and find magnitudes
- Find unit vectors
- Determine direction angles of vectors
- Write vectors in the form $v = a i + b j$ given magnitudes and direction angles
- Solve applied problems involving velocity using vectors
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 |