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.
