Fullerton Joint Union High School District



Mr. Kim’s Syllabus. Room 302. sakim@fjuhsd.k12.ca.us (714) 626-4522

Fullerton Joint Union High School District

COURSE EXPECTATIONS AND GRADING GUIDELINES

Trigonometry/Pre-Calculus

Course Description

Trigonometry/Pre-Calculus is designed to prepare a student for college-level calculus. Topics include trigonometric functions and their graphs, the fundamental identities, inverse trig functions and equations, circular and polar equations, limits, and other advanced topics. Practical applications including the study of right and oblique triangles and vectors are emphasized.

District Content Standards for Trigonometry/Pre-Calculus

Trigonometric Functions and Applications

1. Students understand the concept of angle, and how to measure it, both in degrees and radians. They can convert between degrees and radians.

2. Students know the definition of sine and cosine as y and x coordinates of points on the unit circle, and are familiar with the graphs of the sine and cosine functions.

3. Students know the definition of the six trig functions given a point on the terminal side of an angle.

4. Students can

1. prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity using the Pythagorean theorem, and conversely they can prove the Pythagorean theorem as a consequence of this identity).

2. prove other trigonometric identities, and simplify them using the identity cos2x + sin2x = 1 (e.g., students use this identity to prove that sec2(x)= tan2(x) + 1).

3. prove the sum and difference identities, and are able to use them to simplify other trig identities.

4. demonstrate understanding of double angle, power reducing, and half angle identities for sine, cosine, and tangent and can use them to prove and/or simplify

5. Students graph functions of the form [pic]and interpret in terms of amplitude, frequency, period, phase shift, and vertical shift.

6. Students know the definition of the tangent and cotangent functions, and can graph them.

7. Students know the definitions of the secant and cosecant functions, and can graph them.

8. Students know that the tangent of the angle of inclination of a line is equal to the slope of the line.

9. Students know the definitions of the inverse trigonometric functions, and can graph the functions.

10. Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

11. Students use trigonometry to determine unknown sides or angles in right triangles.

12. Students know the Laws of Sines and the Law of Cosines, and apply them to problems.

13. Students determine the area of a triangle given one angle and the two adjacent sides or all three sides.

14. Students can determine the polar coordinates of a point given in rectangular coordinates, and vice versa.

1. Students convert between rectangular equations and polar equations.

2. Students should be able to recognize and graph standard polar equations.

15. Students can represent a complex number in trigonometric/polar form and graph it.

1. Students know how to perform basic operations on complex numbers in rectangular form.

2. Students know how to perform basic operations on complex numbers in trigonometric/polar form.

3. Students know De Moivre’s Theorem, and can give n-th roots of a complex number given in polar form.

16.0 Students are adept at using trigonometry in a variety of applications and word problems.

Mathematical Analysis

1. Students have knowledge of a vector and can represent it graphically.

1. Students can perform operations on vectors.

2. Students can apply vectors to physical problems.

2. Students are familiar with and can apply polar coordinates and vectors in the plane.

3. Students demonstrate understanding of the geometric interpretation of vectors and vector addition (via parallelograms) for vector in the plane.

4. Students are familiar with conic sections, both analytically and geometrically.

5. Students can take a quadratic equation in two variables and when necessary use transformation properties to determine the type of conic section the equation represents and list its geometric components.

1. Students can take a geometric description of a conic section (e.g., the locus of points whose sum of its distances from (1,0) and (-1, 0) is 6), and derive a quadratic equation representing it.

6. Students find the roots of a rational function, can graph the function, and can locate its asymptotes.

7. Students demonstrate an understanding of functions and equations defined parametrically, and can graph them.

Linear Algebra

1. Students apply the method of mathematical induction to prove general statements about the positive integers.

2. Students reduce rectangular matrices to row echelon form.

3. Students perform addition and multiplication on matrices.

4. Students demonstrate understanding of the notion of the inverse to a square matrix, and apply it to solve systems of linear equations.

Functions

1. Students determine whether a relation defined by a graph, a set of ordered pairs, or symbolic expression is a function and justify the conclusion.

2. Students determine the domain of independent variables, and range of dependent variables, and range of dependent variables defined by a graph, a set of ordered pairs, or symbolic expression.

3.0 Students will be able to perform operations on functions including compositions.

4.0 Students will perform transformations on functions and show the modification of their graphs.

Exponential and Logarithmic Functions

1.0 Students know the laws of exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

2.0 Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents.

3.0 Students understand and apply the laws of logarithms.

Sequences, Series and Limits

1.0 Students find the general terms and the sums of arithmetic series and both finite and infinite geometric series.

2.0 Students apply the method of mathematical induction to prove general statements about the positive integers.

3.0 Students are familiar with the limit of a sequence and the limit of a function as the independent variable approaches a number of infinity. They determine if certain sequences converge or diverge.

Course Goals

1. The student will demonstrate an understanding of the six trigonometric functions, their properties and their applications.

2. The student will demonstrate knowledge of vectors and conic sections, and how they apply to real-life situations.

3. The student will perform matrix operations and apply matrices in problem-solving situations.

4. The student will demonstrate an understanding of functions, including their domains, ranges, inverses, and translations.

5. The student will exhibit and understanding of exponential and logarithmic functions.

6. The student will have a basic understanding of sequences, series, and limits.

Class Materials

Book, Paper, Pencil, Eraser, Appropriate Calculator (Which will be addressed at a later time)

All homework headings must be in pen. Heading will include name, period, date, and homework number.

All homework, quizzes, and tests must be in pencil. Assignments in pen will result in zeroes.

Attendance Policy

School policy regarding absences and units apply. Being tardy to class will result in a loss of a participation point unless the student has a written excuse from a teacher or administrator. Multiple truancies will result in detention.

Students will have the number of days they missed to make up late homework. Students are responsible for scheduling make-up tests and quizzes. If a make-up is not discussed on the first day back, a zero will be assumed.

Classroom Expectations

1) Respect the classroom, keep it clean, food, gum, and trash free.

2) Have fun, you are learning math, which is better than not learning math.

3) Homework must be turned in on time. Late homework will not be accepted unless excused.

4) Don’t cut through other classrooms in coming or going to class, it will result in automatic massive point loss (-160).

5) Don’t cheat. It will result in an automatic zero on a test or quiz, along with other possible punishments.

6) Don’t use your phone in class. If caught actually speaking on your phone in class, it will also automatically result in massive point loss (-160). Other uses will result in point loss and possible long term confiscation.

7) Use common sense, if you need some, ask the teacher for help.

Some early pointers

i) Write down the correct homework assignment.

ii) Write down the correct problem.

iii) Double check your work.

8) All other school rules apply.

Grading Policy/Guidelines

A+ 99.00 or higher A 92.50 – 98.99 A- 89.50 – 92.49

B+ 87.90 – 89.49 B 82.50 – 87.89 B- 79.50 – 82.49

C+ 77.90 – 79.49 C 72.50 – 77.89 C- 69.50 – 72.49

D+ 67.90 – 69.49 D 62.50 – 67.89 D- 60.00 – 62.49

F 59.99 or below.

3 points per assignment. 240 points

40 points per quiz 160 points

4 tests 800 points

300 point final 300 points

50 points miscellaneous (Group presentations, projects) 50 points

50 points participation. (can go below 0/50) 50 points = 1600 points

Participation Points

When the signature is returned, the student will be credited with 50 points for participation. Students will keep them as long as they are on time, participate in class, do not break rules, and are diligent in their work. Students lose points when they are unprepared, disruptive, or break rules. Participation may go below 0 points if they commit many offenses or one of the major ones above.

Kim dollars

This is your bathroom, late homework, and one minute tardy pass. They can be earned. At the end of the semester, each one will be worth one point. If reproduction of dollars is suspected, all dollars will retain a value of zero for everyone in class.

Miscellaneous

E-mail is the best way to reach me, unless the e-mail server goes down.

I reserve the right to make changes as necessary.

Trigonometry/Pre-Calculus

Student and Parent Signatures

This verifies that I have read and understood the above information as it was explained in the handout and discussed in class.

Student Name _________________________________________ Date ____________

(please print)

Student Signature _______________________________________________________

This verifies that I have read and discussed the above information with my son or daughter.

Parent/Guardian Name _________________________________ Date ____________

(please print)

Patent/Guardian Signature ________________________________________________

Telephone Number ________________________ Email ________________________

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