Functions UnitApplications UnitCircle Trig Unit Identities UnitTrig. Equations UnitComplex Numbers Unit Pre-course ReflectionPost-course Reflection I am

Functions Unit Applications Unit Circle Trig Unit Identities Unit Trig. Equations Unit Complex Numbers Unit

Pre-course Reflection Post-course Reflection

I am part Scottish

I was born in Temecula, California I have

played soccer for 6

years.

Pre-course reflections page

Write a short paragraph (50~75 words) describing your feelings about math classes in general prior to this course (likes/dislikes) and what your

expectations are for this course.You may include images but they are not required.

Pre-Course Reflections


Functions Unit Applications Unit Circle Trig Unit

Identities Unit Trig. Equations Unit Complex Numbers Unit

(Unit 1): Trigonometric Functions 1. Angles and Degree Measure; Angles and Rotation – Objective: To use definitions of angles and

their parts, to identify the direction of an angle’s rotation, and to find an angle’s portion of full circular rotation.

2. Radian Measure – Objective: To understand the origin of and definition of radian measure, and to be able to convert freely between radian and degree measures.

3. Arc Length / Sector Area Applications – Objective: To calculate the length of a circular arc and a circular sector area for problems where measurements are given in either degree or radian measure.

4. Trigonometric Ratios; Definition of Trigonometric Functions – Objective: To identify the sine, cosine, and tangent of an angle in a right triangle (SOHCAHTOA).

5. Function Values of Special Angles – Objective: To recall the exact trigonometric function values for the quadrantal angles and the 45°, 30°, and 60° angles (and their radian equivalents).

6. Function Values of Acute Angles – Objective: To find the values of trigonometric functions from tables and/or calculators.

7. Finding Acute Angles from Function Values – Objective: To find the acute reference angle from the given trigonometric values from a table and/or calculator (eg. arcsin, sin -1)

Functions Unit




Sample Work

Pick an objective from the unit and place sample work on this slide addressing that objective. Sample work may include the following:

Copies of homeworkCopies of quizzes or examsCopies of a project

You may attach images of these pages or thumbnails of an image stored elsewhere electronically. If using a thumbnail, be sure to provide a link so others can view the full sized image.

For each piece of sample work, write a short narrative describing the purpose of the work, what you did well and what you found challenging.

This may take more than one slide, so feel free to insert duplicate slides following this one as needed to showcase your work.

Functions Unit




Sample Work: continued

Functions Unit




Real-World Application

Choose a topic from this unit and briefly describe how this topic is applied outside of this course. The application can

be for a different course or a use “on the job.” You may include images, and/or links to websites to help illustrate

your description.

Functions Unit




(Unit 2): Applications of (plane) trigonometry1. Arc Length and Sector Area – Objective: To find arc lengths and sector areas of circles for real-world

problems in such fields and astronomy and surveying.2. Solutions of Right Triangles – Objective: To practice using the trigonometric functions to find all side

lengths and angle measures given any three of the six measures.3. Geometric Applications – Objective: To solve for the physical measurements of real-world problems

using the trigonometric functions.4. Surveying Applications – Objective: To solve for the physical measurements of surveying problems

and to learn the definitions of “angle of elevation” and “angle of depression”.5. Navigation Applications – Objective: To learn the terminology of navigation and solve problems

related to this field.6. Vectors - Objective: To find the components of vectors and apply this concept with vector addition

to solve problems.7. Law of Sines -Objective: To learn the law of sines, and its restrictions, and apply the law to real-

world situations.8. Law of Cosines - Objective: To learn the law of cosines and apply it to solving real-world problems.9. Outside Activity - Objective: To provide hands-on instruction in measuring angles and in solving a

surveying problem using field observations.

Applications Unit




Applications Unit - Sample Work:


Copies of homeworkCopies of quizzes or exams

You may attach images of these pages or thumbnails of an image stored elsewhere electronically. If using a thumbnail, be sure to provide a link so someone can view the full sized image.

For each piece of sample work, write a short narrative describing the purpose of the work, what you did well and what areas could have been improved upon.


Applications Unit





Applications Unit







your description.

Applications Unit




(Unit 3) Circular Trigonometry1. Unit Circle; Definitions - Objective: To define the unit circle and the

angles on it.2. Reference Angle - Objective: To convert angles measured on the unit

circle into acute angles with congruent trigonometric values.3. Graphs of sin(x) and cos(x) - Objective: To graph the functions of

sine and cosine and understand the cyclic nature of their graphs.4. Graphs of Asin(Bx) and Acos(Bx) - Objective: To extend the lesson

above to include a function’s amplitude and period (width) of a cycle.

5. Phase Shift and Biorhythms - Objective: To extend the lesson above to include a function’s lateral and vertical shift, and to practice graphing a sine wave via a plotting of one’s biorhythms.

Circle Trig Unit




Circle Trig Unit




In this assignment we were to create a worksheet for a student to use to practice graphing sine waves. We had to include the worksheet, an answer form and show common mistakes students make when graphing (then fix these mistakes). I did well on this paper and met all requirements. The worksheet could’ve been darker. (click on the page to open it)

Circle Trig Unit




For this homework assignment we had practiced graphing a sine wave by calculating our biorhythms. This page is the part where we had to graph the wave for some day that was memorable to see if the biorhythm matched. The event was an emotional one, and the emotional wave almost crossed the critical line on that day, so it was close.

Circle Trig Unit




On this quiz I did pretty well on the front side. My mistake on the back was that I graphed the second wave as a cosine wave and the period was wrong. I knew how to calculate the period but didn’t graph it right. (click on the quiz to see the whole thing)

Circle Trig Unit




This is the Unit Test. I did well on this exam and even got the coveted, “N.C.” on my graphs The mistakes I made were not listing ALL of the x-intercepts from 0 to 2 pi. I only listed those from the first wave. (click on the test to see the whole thing)




your description.

Circle Trig Unit




(Unit 4) Trigonometric Identities1. Basic Identities - Objective: To practice memorizing the reciprocal, quotient and

Pythagorean identities while manipulating trigonometric equations with algebra.2. Negative Angle Identities - Objective: To convert trigonometric expressions involving

negative angles into expressions involving positive angles and to use this knowledge to simplify trigonometric expressions.

3. Cosine of a Sum or Difference - Objective: To recognize and utilize this identity in order to simplify and manipulate complicated trig. expressions.

4. Complementary Identities - Objective: To understand the relationship between sine, secant, tangent and their respective cof-unctions, and to use this understanding to simplify complicated trig. expressions.

5. Sine of a Sum or Difference -Objective: To recognize and utilize this identity in order to simplify and manipulate complicated trig. expressions.

Identities Unit




Identities Unit - Sample Work:






Identities Unit





Identities Unit







your description.

Identities Unit




(Unit 5) Solving Trigonometric Equations1. Trigonometric Equations ~ Elementary Form - Objective:

To solve trig. equations by considering all values which will make true a given equation (emphasis on the cyclic nature of the solution set).

2. Trigonometric Equations ~ Factoring Method - Objective: To use factoring as a method to simplify complicated trigonometric equations before solving.

3. Trigonometric Equations ~ Identity Method - Objective: To use trigonometric identities as a method to simplify complicated equations before solving.

Trig Equations Unit




Trig Equations Unit - Sample Work:






Trig Equations Unit





Trig Equations Unit







your description.

Trig Equations Unit




(Unit 6) Complex Numbers / Polar Coordinates1. Definitions and Graphing of Complex Numbers - Objective: To recall the definitions of

complex numbers and to express these numbers graphically on a coordinate plane.2. Polar Coordinates - Objective: To freely convert between the rectangular and polar

coordinates of points on a coordinate plane.3. Trigonometric Form of Complex Numbers - Objective: To recognize the similarities

between the trig. form of complex numbers and polar coordinates of points on a plane and use this recognition to convert complex numbers to trigonometric form and vice-versa.

4. Products and Quotients of Numbers Expressed in Trig. Form - Objective: To multiply and divide numbers expressed in trigonometric form.

5. Powers and Roots of Complex Numbers ~ DeMoivre’s Theorem - Objective: To simplify numbers with large exponents, and to find all roots of complex numbers by use of DeMoivre’s Theorem.

Complex Numbers Unit




Complex Numbers Unit - Sample Work:


















your description.





Post-course Reflections

Short summary of what you liked about this course, things you remember about the course and what you liked best about the course. You may need

to use more than one slide. Images may be included but are not necessary. Word count is 250 words or more.

Post-Course Reflections




Post-course Reflectionscontinued





Post-course Reflectionscontinued





Documents

Functions UnitApplications UnitCircle Trig Unit Identities UnitTrig. Equations UnitComplex Numbers Unit Pre-course ReflectionPost-course Reflection I am