TRIGONOMETRY/STATISTICS
CURRICULUM

This course is designed for students who have taken Algebra II or Algebra II/Trigonometry.  The first semester of the course provides a thorough study of trigonometric functions, equations, graphs, and applications.  The second semester is designed to introduce students to important concepts of statistics and probability.  Students will take full advantage of technology to collect, analyze, and display their own data.  Projects are an integral part of this course.  Many careers require a strong background in statistics.  The prerequisite for this course is the successful completion of Algebra II or Algebra II/Trigonometry.

Learning Objectives
    The student will:
        Demonstrate the following skills

Basic trigonometric identities
    The student will:
        Verify basic trigonometric identities and make substitutions using the basic identities.

Trigonometric functions
    The student will:
        Use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant and cosecant of an angle in standard position, given a point, other than the origin, on the terminal side of the angle.
        Circular function definitions will be connected with trigonometric function definitions.
        Given the value of one trigonometric function, will find the values of the other trigonometric functions.
        Properties of the unit circle and definitions of circular functions will be introduced.
        Find the values of  the trigonometric functions of the special angles and their related angles as found in the unit circle without the aide of a calculating utility.
        Converting radians to degrees and vice versa.
        Use a calculator to find the value of any trigonometric function and inverse trigonometric function.

Trigonometric equations
    The student will:
        Solve trigonometric equations that  include both infinite solutions and restricted domain solutions and solve basic trigonometric inequalities.
        Graphing utilities will be used to solve equations, to check for reasonableness of results, and to verify algebraic solutions.

Triangles
    The student will:
        Identify, create, and solve practical problems involving triangles.
        Techniques will include using the trigonometric functions, Pythagorean Theorem, the Law of Sines, and the Law of Cosines.
 

Statistics
    The student will:
        Calculate measures of center and spread for data sets.
        Students will use notation to represent a sum, mean, variance, and standard deviation.
        Describe relations between measures of center or measures of spread.
        Use samples to make inferences about populations.
        Determine relationships and interpret data presented in a table or graph.  Analysis and interpretation of data.
        Use statistics to compare and contrast data sets.
        Design their own surveys utilizing random sampling techniques and employing statistical methods to interpret data.
        Learn to criticize and scrutinize statistical information presented by the press.
        Apply normal distribution and hypothesis testing to data with a standard deviation.
        Collect and analyze data to make predictions, write equations, and solve practical problems.
    NOTE: Graphing calculators will be used to investigate scatter plots, box and whisker plots, and histograms. Spreadsheets will also be used.
 

Probability
    The student will:
        Use areas under the standard normal curve to find probabilities.
        Identify sample spaces and events in probabilistic experiments calculating the probability of outcomes.
    NOTE: Consideration will be taken of mutually exclusive, independent, and complementary events.
        Differentiate between permutations and combinations, calculating permutations and combinations.
        Construct, graph, and interpret probability distributions.
        Build a binomial distributor.
        Investigate various lottery schemes and casino games.