MTH 167 Pre-Calculus with Trigonometry (5 cr.)
Presents topics in power, polynomial, rational, exponential, and logarithmic functions, systems of equations, trigonometry, trigonometric applications, including Law of Sines and Law of Cosines and an introduction to conics. Credit will not be awarded for both MTH 167 and MTH 161/162. Lecture 5 hours per week.
Major Topics:
Relations and Functions
Polynomial and Rational Functions
Exponential and Logarithmic Functions
Systems of Equations
Trigonometric Functions
Analytic Trigonometry
Applications of Trigonometry
Sequences and Series
Conics
Objectives and Skills:
Distinguish between relations and functions
Evaluate functions both numerically and algebraically
Determine the domain and range of functions, including root and rational functions
Perform arithmetic operations on functions, including composition of functions and the difference quotient
Identify and graph linear, absolute value, quadratic, cubic, and square root functions
Determine and verify inverses of one-to-one functions
Determine the general and standard forms of quadratic functions
Use formula and completing the square method to determine the standard form of a quadratic function
Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions
Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials
Determine if a function has even or odd symmetry
Use Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine all zeros
Identify intercepts, end behavior, and asymptotes of rational functions
Solve polynomial and rational inequalities
Interpret the algebraic and graphical meaning of equality of functions f(x) = g(x) and inequality of functions f(x) > g(x)
Decompose partial fractions of the form P(x)/Q(x) where Q(x) is a product of linear factors
Identify and graph exponential and logarithmic functions
Use properties of logarithms to simplify and expand logarithmic expressions
Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms
Solve exponential and logarithmic equations using one-to-one and inverse properties
Solve application problems involving exponential and logarithmic functions
Solve three variable linear systems of equations using the Gaussian elimination method
Identify angles in standard form in both degree and radian format and convert from one to the other
Find the arc length
Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry
Use reference angles to evaluate trig functions
Find the value of trigonometric functions of angles using a calculator
Use fundamental trigonometric identities to simplify trigonometric expressions
Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts
Use trig functions to model applications in life and natural sciences
Use fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities
Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions
Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions
Solve trigonometric equations over restricted and non-restricted domains
Solve right triangles and applications involving right triangles
Use the Law of Sines and Law of Cosines to solve oblique triangles and applications
Apply concepts of trigonometry to extended topics such as plotting polar coordinates, converting rectangular and polar coordinates from one to the other, identifying vector magnitude and direction, or performing operations with vectors such as addition, scalar multiplication, component form, and dot product
Identify the terms of geometric sequences
Find a particular term of geometric sequence
Determine the formula for the n-th term of geometric sequences
Find the sum of first n terms of finite geometric series
Find the sum of infinite geometric series
Identify various conic section forms
Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin
Graph equations of conic sections centered at the origin or not at the origin
Solve applications involving conic sections