10-31-2023 Chapter 7 Part 3

Class Notes

Topics Covered:

  • Double-angle identities: Problem type 1

  • Double-angle identities: Problem type 2

  • Power-reducing identities

  • Proving trigonometric identities using double-angle identities: Problem type 1

  • Proving trigonometric identities using double-angle identities: Problem type 2

  • Half-angle identities: Problem type 1: Degrees

  • Half-angle identities: Problem type 1: Radians

  • Half-angle identities: Problem type 2

10-26-2023 Chapter 7 Part 2

Class Notes

Topics Reviewed:

  • Proving an identity using fundamental trigonometric identities: Problem type 5

  • Proving an identity using fundamental trigonometric identities: Problem type 6

  • Proving an identity using fundamental trigonometric identities: Problem type 7

  • Proving trigonometric identities using odd and even identities

  • Sum and difference identities: Problem type 2: Degrees

  • Sum and difference identities: Problem type 3

  • Proving trigonometric identities using sum and difference identities: Problem type 1

  • Proving trigonometric identities using sum and difference identities: Problem type 3

10-24-2023 Chapter 7 Part 1

Class Notes

Topics Covered:

  • Using cofunction identities

  • Finding values of trigonometric functions given information about an angle: Problem type 3

  • Using reciprocal and quotient identities to simplify a trigonometric expression

  • Using Pythagorean identities to simplify a trigonometric expression

  • Verifying a trigonometric identity: Problem type 1

  • Verifying a trigonometric identity: Problem type 2

  • Verifying a trigonometric identity: Problem type 3

  • Proving an identity using fundamental trigonometric identities: Problem type 1

  • Proving an identity using fundamental trigonometric identities: Problem type 2

  • Proving an identity using fundamental trigonometric identities: Problem type 3

  • Proving trigonometric identities using odd and even identities

10-12-23 Chapter 6 Part 4

Class Notes

Topics Covered:

  • Evaluating a sinusoidal function that models a real-world situation

  • Word problem involving a sine or cosine function: Problem type 1

  • Developing a sinusoidal model for a real-world situation

  • Sketching the graph of a sinusoidal function that models a real-world situation and using the graph to approximate solutions to an equation

  • Using trigonometry to find a length in a word problem with one right triangle

  • Using trigonometric functions and the formula d = rt in a real-world situation

  • Using trigonometry to find angles of elevation or depression in a word problem

  • Using trigonometry to find lengths in a figure involving two right triangles

  • Using trigonometry to find a length in a word problem with two right triangles

10-10-23 Chapter 6 Part 3

Class Notes

Topics Covered:

  • Sketching the graph of y = a sin(x) or y = a cos(x)

  • Sketching the graph of y = sin(bx) or y = cos(bx)

  • Using transformations to graph y = ±sin(bx) or y = ±cos(bx)

  • Sketching the graph of y = a sin(bx) or y = a cos(bx)

  • Amplitude and period of a sine or cosine function

  • Matching graphs and equations for secant, cosecant, tangent, and cotangent functions

  • Sketching the graph of a secant or cosecant function: Problem type 1

  • Sketching the graph of a tangent or cotangent function: Problem type 1

  • Evaluating a sinusoidal function that models a real-world situation

  • Sketching the graph of y = sin(x) + d or y = cos(x) + d

  • Using transformations to graph y = ±sin(x) + d or y = ±cos(x) + d

  • Using transformations to graph y = a sin(x) + d or y = a cos(x) + d

  • Using transformations to graph y = ±sin(bx) + d or y = ±cos(bx) + d

  • Using graphing to solve a trigonometric equation involving sine or cosine

  • Sketching the graph of y = sin(x+c) or y = cos(x+c)

  • Sketching the graph of y = a sin(x+c) or y = a cos(x+c)

  • Using transformations to graph y = a sin(x+c) + d or y = a cos(x+c) + d

  • Using transformations to graph y = sin(bx+c) or y = cos(bx+c)

  • Sketching the graph of y = a sin(bx+c) or y = a cos(bx+c)

  • Sketching the graph of y = a sin(bx) + d or y = a cos(bx) + d (4m)

  • Using transformations to graph y = a sin(bx+c) + d or y = a cos(bx+c) + d (4m 30s)

  • Amplitude, period, and phase shift of a sine or cosine function (2m)

  • Understanding how changes to the amplitude, period, phase shift, and vertical shift affect a sinusoidal graph (2m)

  • Sketching the graph of a secant or cosecant function: Problem type 2 (5m 30s)

  • Sketching the graph of a tangent or cotangent function: Problem type 2 (5m)

10-5-2023 Chapter 6 Part 2

Class Notes

Topics Covered:

  • Drawing an arc to find a central angle or an arc length on the unit circle

  • Finding coordinates on the unit circle for special angles

  • Finding a point on the unit circle given one coordinate and the quadrant

  • Using the coordinates of points on the unit circle to define sine and cosine for all real numbers

  • Special triangles with a hypotenuse of length 1

  • Drawing a reference triangle on the unit circle and using it to derive values of trigonometric functions: Radians

  • Trigonometric functions and special angles: Problem type 1: Radians

  • Finding values of trigonometric functions from a point on the unit circle

  • Trigonometric functions and special angles: Problem type 2

  • Using the coordinates of points on the unit circle to define trigonometric functions for all real numbers

  • Trigonometric functions and special angles: Problem type 3

  • Evaluating expressions involving sine or cosine

  • Sketching an angle with absolute value less than 2π radians, and also its reference angle

  • Reference angles in radians: Problem type 1

  • Sketching an angle with absolute value greater than 2π radians, and also its reference angle

  • Reference angles in radians: Problem type 2

  • Using the unit circle to understand that sine and cosine are periodic

  • Using symmetries on the unit circle to understand trigonometric identities: Problem type 2

  • Using the unit circle to understand the odd and even identities for sine and cosine

10-2-2023 Chapter 6 Part 1

Class Notes

Topics Covered:

  • Similar polygons

  • Indirect measurement

  • Converting degrees-minutes-seconds to decimal degrees

  • Converting decimal degrees to degrees-minutes-seconds

  • Converting degrees to radians and radians to degrees: Problem type 1

  • Converting degrees to radians and radians to degrees: Problem type 2

  • Sketching an angle with absolute value less than 360 degrees in standard position

  • Sketching an angle with absolute value less than 2π radians in standard position

  • Sketching an angle in standard position given in degrees and finding a coterminal angle

  • Sketching an angle in standard position given in radians and finding a coterminal angle

  • Coterminal angles

  • Arc length and central angle measure

  • Relating an angle and an arc length in a real-world situation

  • Relating two angle measures in a real-world situation that involves interlocking gears

  • Area of a sector of a circle

  • Using the area formula for a sector of a circle in a real-world situation

  • Angular and linear speed

9-19-2023 Chapter 4 Part 3

Class Notes

Topics Covered:

  • Domain of a rational function: Interval notation

  • Finding the asymptotes of a rational function: Constant over linear

  • Finding the asymptotes of a rational function: Linear over linear

  • Finding horizontal and vertical asymptotes of a rational function: Quadratic numerator or denominator

  • Graphing a rational function: Constant over linear

  • Graphing a rational function: Linear over linear

  • Matching graphs with rational functions: Two vertical asymptotes

  • Writing the equation of a rational function given its graph

  • Finding x- and y-intercepts of the graph of a nonlinear equation

  • Finding the asymptotes of a rational function: Quadratic over linear

  • Graphing a rational function: Quadratic over linear

  • Graphing rational functions with holes

  • Graphing a rational function with more than one vertical asymptote

9-14-2023 Chapter 4 Part 2

Class Notes

Topics Covered:

  • Finding zeros of a polynomial function written in factored form

  • Finding zeros and their multiplicities given a polynomial function written in factored form.

  • Multiplying expressions involving complex conjugates

  • Finding a polynomial of a given degree with given zeros: Real zeros

  • Finding a polynomial of a given degree with given zeros: Complex zeros

  • Using the rational zeros theorem to find all zeros of a polynomial: Irrational zeros

  • Using a given zero to write a polynomial as a product of linear factors: Complex zeros

  • Using the rational zeros theorem to find all zeros of a polynomial: Complex zeros

  • Using a graphing calculator to find local extrema of a polynomial function

  • Using a graphing calculator to solve a word problem involving a local extremum of a polynomial function

  • Determining the end behavior of the graph of a polynomial function

  • Inferring properties of a polynomial function from its graph

9-12-2023 Class Chapter 4 Part 1

Class Notes

Topics Covered:

  • Domain of a rational function: Interval notation

  • Solving a quadratic inequality written in factored form

  • Solving a quadratic inequality

  • Polynomial long division: Problem type 1

  • Polynomial long division: Problem type 2

  • Polynomial long division: Problem type 3

  • Synthetic division

  • Using the remainder theorem to evaluate a polynomial

  • The Factor Theorem

  • Finding a polynomial of a given degree with given zeros: Real zeros

  • Using a given zero to write a polynomial as a product of linear factors: Real zeros

  • Finding all possible rational zeros using the rational zeros theorem: Problem type 1

  • Finding all possible rational zeros using the rational zeros theorem: Problem type 2

  • Using the rational zeros theorem to find all zeros of a polynomial: Rational zeros

  • Using the rational zeros theorem to find all zeros of a polynomial: Irrational zeros

9-7-2023 Class

Class Notes

Topic List:

  • Sum, difference, and product of two functions

  • Quotient of two functions: Basic

  • Quotient of two functions: Advanced

  • Combining functions: Advanced

  • Finding a difference quotient for a linear or quadratic function

  • Introduction to the composition of two functions

  • Composition of two functions: Basic

  • Composition of a function with itself

  • Expressing a function as a composition of two functions

  • Composition of two functions: Domain and range

  • Composition of two functions: Advanced

  • Composition of two rational functions

  • Word problem involving composition of two functions

  • Finding the roots of a quadratic equation with leading coefficient greater than 1

  • Solving a rational equation that simplifies to linear: Denominator x

  • Horizontal line test

  • Determining whether two functions are inverses of each other

  • Inverse functions: Linear, discrete

  • Inverse functions: Quadratic, square root

  • Inverse functions: Cubic, cube root

  • Inverse functions: Rational

  • Graphing the inverse of a function given its graph

  • Finding, evaluating, and interpreting an inverse function for a given linear relationship

9-5-2023 Class

Class Notes

Topics Covered

  • Finding the vertex, intercepts, and axis of symmetry from the graph of a parabola

  • Determining if graphs have symmetry with respect to the x-axis, y-axis, or origin

  • Testing an equation for symmetry about the axes and origin

  • Finding local maxima and minima of a function given the graph

  • Finding the absolute maximum and minimum of a function given the graph

  • Finding values and intervals where the graph of a function is zero, positive, or negative

  • Graphing an absolute value equation of the form y = A|x|

  • Graphing a cubic function of the form y = ax3

  • Graphing a function of the form f(x) = ax2

  • Graphing a function of the form f(x) = ax2 + c

  • Graphing a parabola of the form y = (x-h)2 + k

  • Graphing a square root function: Problem type 1

  • Graphing a cube root function

  • Translating the graph of a parabola: One step

  • Translating the graph of a parabola: Two steps

  • How the leading coefficient affects the shape of a parabola

  • Translating the graph of an absolute value function: One step

  • Translating the graph of an absolute value function: Two steps

  • How the leading coefficient affects the graph of an absolute value function

  • Writing an equation for a function after a vertical translation

  • Translating the graph of a function: One step

  • Translating the graph of a function: Two steps

  • Transforming the graph of a function by reflecting over an axis

  • Transforming the graph of a function by shrinking or stretching

  • Transforming the graph of a function using more than one transformation

  • Transforming the graph of a quadratic, cubic, square root, or absolute value function

8-31-2023 Class Chapter 1 Topics

Topics Covered

  • Finding x- and y-intercepts of a line given the equation: Advanced

  • Writing the equation of a line through two given points

  • Writing and evaluating a function that models a real-world situation: Advanced

  • Writing an equation and drawing its graph to model a real-world situation: Advanced

  • Finding the intercepts and rate of change given a graph of a linear function

  • Choosing a graph to fit a narrative: Advanced

  • Identifying parallel and perpendicular lines from equations

  • Identifying parallel and perpendicular lines from coordinates

  • Identifying coordinates that give right triangles

  • Evaluating functions: Absolute value, rational, radical

  • Domain and range from the graph of a continuous function

  • Domain of a rational function: Interval notation

  • Domain of a square root function: Advanced

  • Finding where a function is increasing, decreasing, or constant given the graph

    Class Notes

First Class Information and Syllabus

Welcome to the Fall 2023 Semester.

Office Hours will be held on Tuesday and Thursday from 12:30 to 2:15 in room E221 and online on Google Meet.

Here is the syllabus - Fall 2023 MATH1610 Syllabus

In the syllabus you will find the grading policy and the important dates. You will also find the financial aid code which will give you 2 weeks to get your ALEKS code. You do not need the physical book unless you want it all you need is the code and it will give you access to the e-book.

Your Class Code is: AFPE3-GEF4W