Course
Number: MS101
Course Title:
Algebra and Trigonometry
STUDENT LEARNING OUTCOMES
General
Students
will be able to model and solve equations involving exponential, logarithmic
and trigonometric expression
Specific
Students will be able to:
1.
Work with Exponential Functions
Evaluate exponential expressions by hand and using technology.
Identify the parameters of an exponential function.
Identify transformations of exponential functions.
Graph exponential functions
Define the number e.
Calculate interest amounts using compound interest.
Calculate interest amounts using continuous compounding.
Recognize that a function is growing/decaying
exponentially.
2.
Work with Logarithmic Functions
Define the meaning of the logarithm base a
Evaluate logarithmic expressions by hand and using technology.
Understand the properties of logarithms.
Graph logarithmic functions.
Recognize transformations of logarithmic functions.
Use the change of base formula.
Use the properties of logarithms to expand logarithmic
expressions.
Use the properties of logarithms to condense logarithmic expressions.
Explain the inverse relationship between exponential and
logarithms.
3.
Work with Equations involving exponentials and
Logarithms
Use logarithms to solve exponential equations.
Use exponentials to solve logarithmic equations.
4.
Work with Exponential and Logarithmic Models
Given several data points, model an exponential growth function.
Given several data points, model and exponential decay function.
Find the doubling time of an exponential growth function.
Find the half-life
of an exponential decay function.
Use exponentials and logarithms to solve interest problems.
5.
Work with Angles and Triangle
Describe angles
Use degree measure
Use radian measure
Sketch angles in standard position
Convert between degree and radian measure
Convert between decimal degrees and deg/min/sec format
Determine if two angles are co-terminal
Use the Pythagorean Theorem to find missing sides of triangles
Determine if a triangle is a right triangle
Sketch a triangle given any two sides
Find the six trigonometric ratios of the acute angles in a right
triangle
Construct a 30-60-90 and 45-45-90 triangle from memory
Use technology to find trigonometric ratios of angles using
degrees/radians.
Find a missing side of a right triangle using a trigonometric
ratio
Model physical situations using right triangles.
6.
Work with Trigonometric Ratios
Define the six trigonometric ratios for angles of any measure,
i.e. non-acute angles
Given a point on the terminal ray of an angle, find the
trigonometric rations of the angle.
Describe and sketch the unit circle
Define a reference angle
Find the reference angle of a given angle
Evaluate, by hand, the trig ratios of given angles using a
reference angle
Define a periodic function
Model periodic phenomena using periodic functions
Define a quadrant angle
7.
Work with Graphs of Periodic Functions
Recognize and sketch graphs of sine and cosine functions and
transformations of these functions of the form y = a sin (bx) + c and y = a cos (bx) + c
Identify the period, amplitude and midline of a periodic function
from its graph
Identify the period, amplitude and midline of a periodic function
from its equation
8.
Work with Inverse Trigonometric Functions
Define the inverse trigonometric functions of sine, cosine and
tangent
Evaluate, by hand, expressions involving inverse trig functions
Evaluate, using technology, expressions involving inverse trig
functions
Describe the domain and ranges of inverse trigonometric functions
Apply the inverse properties of trigonometric functions
9.
Work with Trigonometric Identities and
Relationships
Use fundamental identities to simplify trigonometric expressions
Verify trigonometric identities
Factor trigonometric expressions
Solve trigonometric equations using algebraic techniques
Solve trigonometric equations using calculator
Use the Law of
Sine to solve oblique
triangles
Use the Law of Cosine to solve oblique triangles