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
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Daily Schedule
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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: Graphing Polar Equations
Section 10.4: Vectors
Course Coordinator
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