WCS Home
CP Trigonometry / Advanced Math Topics
Faculty and Staff

English
Science
History
Math
Spanish
Art
Culinary Arts

Course Description: This is a preparatory course for students intending to take college level or AP Calculus. This year long course is based primarily on the California State Standards for Trigonometry and Mathematical Analysis. In addition, we will incorporate some probability and statistics, and analytic geometry.

Assessment:  Grades are based on:
20% in-class work

30% homework

50% tests and projects

 

Text: Precalculus 6th Edition

Authors: Larson, Hostetler

Publisher: Houghton Mifflin, 2004

 

Content:

 

Functions and their Graphs

Evaluate functions and find their domains

Analyze graphs of functions

Identify and graph shifts, reflections, and non rigid transformations of functions

Find arithmetic combinations and compositions of functions

Find inverses of functions graphically and algebraically

Polynomial and Rational Functions

Sketch and analyze graphs of quadratic and polynomial functions

Use long division and synthetic substitution to divide polynomials

Determine the number of rational and real zeros

Perform operations with complex numbers and plot

Determine the domain, find asymptotes, and sketch rational functions

Exponential and Logarithmic Functions

Recognize, evaluate, and graph exponential and logarithmic functions

Rewrite logarithmic functions with different bases

Use properties of Logs

Solve exponential and logarithmic equations

Use exponential growth, decay and Gaussian models

Fit exponential and logarithmic models to data

Trigonometric Functions

Describe an angle and convert between degree and radian measures

Identify a unit circle and its relationship to real numbers

Evaluate trigonometric functions of any angle

Use trigonometric identities

Sketch graphs of trigonometric functions

Compositions of trigonometric functions

Model real life problems using trigonometric functions

Analytic Trigonometry

Use fundamental identities to evaluate trigonometric functions

Verify trigonometric identities

Solve trigonometric equations using inverses

Use sum an difference formulas, product and sum formulas, multi-angle formulas, power reducing formulas, half-angle formulas to rewrite and evaluate trigonometric functions.

Additional topics in Trigonometry

Use law of sines an cosines

Find areas of oblique triangles

Represent vectors as directed lines and perform mathematical operations on vectors.

Find direction angles of vectors

Find the dot product of two vectors

Multiply and divide complex numbers written in trigonometric form

Find powers and nth root for complex numbers

System of Equations and Inequalities

Solve systems of equations by substitution, by elimination, by Gaussian elimination, and graphically

Recognize linear systems in row-echelon form and to use back substitution to solve the system

Solve nonsquare systems of equations

Sketch the graphs of inequalities in two variables and solve systems of inequalities

Solve linear programming problems

Model real life problems

Matrices and Determinants

Write matrices, identify their order and perform row operations

Use Gaussian elimination and Gaussian-Jordan elimination with matrices to solve a system

Perform operations with matrices

Inverses with matrices

Determinants of square matrices

Uses crammer's rule to solve a system

Sequences, Series, and Probability

Use sequence, factorial, summation notation to writer terms and sums of sequences

Write arithmetic and geometric sequences

Prove statements using induction

Use Binomial Theorem and Pascal’s triangle to calculate binomial coefficients and write binomial expansion

Solve counting problems using the Fundamental Counting Principles, permutations and combinations

Find the probability of events and their complements

Topics in Analytic Geometry

Write the equations, analyze and sketch the graphs of parabolas, ellipses, and hyperbolas

Rotate the coordinate axis to eliminate the xy-term in equations of conics and use the discriminant to identify conics

Solve systems of quadratic equations

Rewrite sets of parametric equations and find sets of parametric equations for graphs

Write equations in polar form, graph polar equations

Write equations of conics in polar form