研究代數第二部分第四部分（共五部分）

In this part of Investigating Algebra two we will be focusing on Rational, radical, and trigonometric functions. We will do this with a combination of lecture, investigation labs, in class application, homework, assignments, and projects

Students will have 3 days of live instruction per week but will be assigned enough work for them to practice the skills 5 days a week. 

Grading: During this class 2 quizzes and a project will be assigned. If sent to teacher, they will be graded. At the end of class all students will receive a certificate of completion. Those who turned in all graded assignments will receive a grade. At the end of part 5 a final will be given. Students who complete the final will get a break down of skills assessment.

Materials
A ruler (12 inches and 30 cm)
Graph paper (Printable provided)
Notebook
Graphing calculator
Workbooks (printable in classroom)

objectives:
Identify direct, inverse, joint, and combined variations.
find the constant of variation and write an equation for the variation
Solve real-world problems involving variations
Identify and evaluate rational functions.
Graph a rational function, find its domain, write equation for its asymptotes, and identify any holes in its graph.
Multiply and divide rational expressions.
Simplify rational expressions, including complex fractions.
Add and subtract rational expressions.
Solve a rational equation or inequality by using algebra, a table, or a graph.
Solve problems by using a rational equation or inequality
Analyze the graphs of radical functions and evaluate radical expressions.
Find the inverse of a quadratic function.
Add, subtract, multiply, divide, and simplify radical expressions.
Rationalize a denominator.
Solve radical equations
solve radical inequalities.
Find the trigonometric Functions of acute angles
Solve a right triangle by using trigonometric functions.
find co-terminal and reference angles.
Find the trigonometric function values of angles in standard position.
find exact values for trigonometric functions of special angles and their multiples
find approximate values for trigonometric functions of any angle
Convert from degree measure to radian measure and vice versa.
Find arc length.
Graph the sine, cosine, and tangent functions.
use the sine function to solve problems.
solve mathematical and real-world problems by using the law of sines and cosines.

Bonus objectives (only taught if time permits)
prove fundamental trigonometric identities
use fundamental trigonometric identities to rewrite expressions
Evaluate expressions by using the sum and difference identities

Schedule subject to change:
Week one: Workbook one: Variations
Week two: Workbook one: Rational expressions and their graphs
Week three: Workbook one: Operations with rational expressions
Week four: Workbook one: solving and simplifying radical expressions
Week five: Workbook two: Right angle trig and angle of rotation
Week six: Workbook two: Trigonometry functions, and radians
Week seven: Workbook two: Law of sines and cosines
Week eight: Bonus workbook: Introduction to trigonometry identities (Time permitting) 

I like to show the students the way math rules work so that it is easier to remember them. This way the curiosity of knowing how something works will move the gears of critical thinking. After I have shown them a pattern and why it works. I will ask them to apply it to a hard problem. If they can use these skills in different ways, I know they have mastered the concepts. I believe to memorize math is not understanding, but to apply math is not only understanding but fluency! To obtain this level of understanding, I will lead the students on a journey to discovering math through discussion, observation, and application of the math being used. If this is the kind of math class, you want then I am the teacher for you.