CURRICULUM MAP: 10108.map
Trigonometry (SCP) 493
25.1 MATHEMATICS - ALG REASONING: PATTERNS & FUNCTS
-- Students will explore and describe patterns and sequences using tables, graphs and charts.
-- Students will describe and compare properties and classes of functions including exponential, polynomial, rational, logarithmic and trigonometric.
-- Students will identify an appropriate symbolic representation for a function or relation displayed graphically or verbally.
-- Students will relate the graphical representation of a function to its function family and find equations, intercepts, maximum or minimum values, asymptotes and line of symmetry for that function.
-- Students will solve problems using concrete, verbal, symbolic, graphical and tabular representations.
-- Students will use logarithms, vectors and matrices to solve problems.
25.1 MATHEMATICS - ALG REASONING: PATTERNS & FUNCTS
-- Students will identify the characteristics of functions and relations including domain and range.
-- Students will use equations to describe the rules for number patterns and to model word problems.
25.2 MATHEMATICS - NUMERICAL & PROP REASONING
-- Students will select and use an appropriate form of number (integer, fraction, decimal, ratio, percent, exponential, scientific notation, irrational, complex) to solve practical problems involving order, magnitude, measures, labels, locations and scales.
-- Students will judge the effects of computations with powers and roots on the magnitude of results.
-- Students will perform operations with complex numbers, matrices, determinants, and logarithms.
-- Students will identify reasonable answers to problems that reflect real world experiences.
-- Students will select and use an appropriate form of number (integer, fraction, decimal, ratio, percent, exponential, scientific notation, irrational) to solve practical problems involving order, magnitude, measures, labels, locations and scales.
-- Students will use technological tools such as spreadsheets, probes, computer algebra systems and graphing utilities to organize and analyze large amounts of numerical information.
25.3 MATHEMATICS - GEOM & MEASUREMT
-- Students will use indirect methods including the Pythagorean Theorem, trigonometric ratios and proportions in similar figures to solve a variety of measurement problems.
-- Students will use properties of similarity and techniques of trigonometry to make indirect measurements of lengths and angles to solve a variety of problems.
-- Students will use the Pythagorean theorem to solve indirect measurement problems.
1. Where and how is trigonometry used in the real world?
2. How can students learn the behavior of and operations on families of functions.
3. How can students demonstrate increased skill in problem solving with applications using these functions?
4. How can students make the connection between radians and degrees, three basic trigonometric graphs and their cofunctions and inverse functions?
Acute angles and right triangles
Radian measure and circular functions
Graphs of the circular functions
Inverse circular functions and trigonometric equations
Applications of Trigonometry and vectors
Complex numbers and polar equations
Exponential and logarithmic functions
Identify angle rotations (from standard position)
Use geometry concepts and similar triangles to determine angle and side relationships
Use Pythagorean Theorem to define the six trigonometric functions
Find functional values using reciprocal, Pythagorean, or quotient identities
Identify signs and ranges of six trigonometric functions
Find functional values of six trigonometric functions for acute and non-acute angles (including special angles) with and without a calculator
Solve applied right angle trigonometry problems using significant digits including angles of elevation or depression and bearing
Convert angle values between degrees and radians as appropriate
Use radian measure to find arc length of a circle including using latitudes to find distance between two cities and area of a sector of a circle
Define trigonometric functions using circular functions
Find values of circular functions with and without exact values
Differentiate between linear and angular speed to solve application problems
Sketch the graphs of sine, cosine, tangent, and other periodic/ circular functions using transformations (shifts and reflections)
Identify and sketch the trigonometric functions with various amplitudes, periods, and translations
Determine a trigonometric model using curve fitting
Using simple harmonic motion identify the amplitude, the period, and the frequency of the motion of a spring
Using fundamental identities find trigonometric functional values given one value and the quadrant
Simplifying and verifying trigonometric identities
Simplifying, identifying, and using sum and difference, double angle, and half angle and cofunction formulas to find exact values
Identify and evaluate inverse trigonometric functions (arc) with and without a calculator
Solve trigonometric equations by linear methods, by factoring, by the quadratic formula
Solve trigonometric equations with half angles or multiple angles
Solving oblique triangles using law of sines or law of cosines with applications
Find the area of a triangle with specific information given
Analyzing data to determine the number of possible triangles with the ambiguous case
Sketching, and operations with vectors,
Finding magnitude and direction of resultant with vectors, and resolving vectors into horizontal and vertical components
Solve equations using complex numbers
Operations with complex numbers
Graph complex numbers and converting between rectangular, trigonometric, and polar forms
Use DeMoivre’s Theorem to find powers of complex numbers
Find roots of complex numbers
Graph an exponential function with a base greater than 1 and an exponential equation with a base between zero and one
Solve equations using properties of exponents
Solve equations using the compound interest formula
Graph a logarithmic function using base 10
Solve a logarithmic equation by converting to exponential form
Simplifying logarithmic expressions using properties of logarithms
Solve applications of logarithms using pH or dec
use a graphing calculator extensively
Students will be assessed by:
1. Daily homework assignments, which will account for 15% of their final grade.
2. Quizzes, approximately one every week
3. Unit tests, comprised of 85-90% computation, 10-15% application
4. Final exam that is comprehensive and will account for 20% of final grade
1. textbook course: Trigonometry (8th ed) by Lial, Hornsby, Schneider
2. Teacher's edition Trigonometry (8th ed)
3. Graphing calculator manual by Nester
4. Instructor's solution manual
5. Student solution manual
6. Course III: Integrated Math textbook
7. Functions modeling Change by Connally textbook for Pre-Calculus